Class 9 Maths - Coordinate Geometry

State to which quadrant does the following points belong:
$D(-3, 2)$

Since the

$x$ -coordinate is negative and

$y$ -coordinate is positive, the point will lie in the

$II$ Quadrant.

State to which quadrant does the following points belong:
$K\left(\dfrac{7}{2}, \dfrac{3}{2}\right)$

Since both the

$x$ -coordinate and

$y$ -coordinate are positive, the point will lie in the

$I$ Quadrant.

State to which quadrant does the following points belong:
$Q(-5, -2)$

Since both the

$x$ -coordinate and

$y$ -coordinate are negative, the point will lie in the

$III$ Quadrant.

State to which quadrant does the following points belong:
$S(-4, 5)$

Since the

$x$ -coordinate is negative and

$y$ -coordinate is positive, the point will lie in the

$II$ Quadrant.

State to which quadrant does the following point belong: $A(2, 3)$

(Enter the integer value to whichever quadrant it belongs to, For example for III quadrant enter 3)

Since both the

$x$ -coordinate and

$y$ -coordinate are positive, the point will lie in the

$I$ Quadrant

State to which quadrant does the following points belong:
$U(-6.2, 4.3)$

Since

$x$ -coordinate is negative and

$y$ -coordinate is positive, the point will lie in the

$II$ Quadrant.

Hence, the answer is

$2$ .

In which quadrant (in number) or on which axis will $(x, y)$ lie if $x>0$ and $y<0$ ?

We know,

in $I$ quadrant both $x$ and $y$ are positive,
in $II$ quadrant $x$ is negative and $y$ is positive,
in $III$ quadrant both $x$ and $y$ are negative
and in $IV$ quadrant $x$ is positive and $y$ is negative.

Given, $x > 0, y < 0$ .

That is, $x$ is positive and $y$ is negative.

Hence, the given point $(x,y)$ lies in the $IV$ th quadrant.

Therefore, $4$ is the answer.

In which quadrant (in number) or on which axis will $(x, y)$ lie if $x>0$ and $y>0$ ?

We know,

Given, $x > 0, y > 0$ .

That is, $x$ is positive and $y$ is positive.

Hence, the given point $(x,y)$ lies in the $I$ st quadrant.

Therefore,

$1$ is the answer.

In which quadrant (in number) or on which axis will $(x, y)$ lie if $x<0$ and $y>0$ ?

We know,

Given, $x < 0, y > 0$ .

That is, $x$ is negative and $y$ is positive.

Hence, the given point $(x,y)$ lies in the $II$ nd quadrant.

Therefore, $2$ is the answer.

$x$ co-ordinate is positive and $y$ co-ordinate is negative ?

When x-co-ordinate is positive and y-co-ordinate is negative , point will lie in IV quadrant

In which quadrant does the point lie if both the co-ordinates are positive?

When both cordinates are positive, point lies in

$I$ quadrant

In which quadrant does the point lie if both the co-ordinates are negative ?

When both cordinates are negative, the point lies in the

$III$ Quadrant.

State to which quadrant does the following points belong:
$L(3, -7)$ (Enter the integer value to which ever quadrant it belongs to, For example for III quadrant enter 3)

Since both the

$x$ -coordinate is positive and

$y$ -coordinate is negative, the point will lie in the

$IV$ Quadrant.

State to which quadrant does the following points belong:
$M(-4, -1)$

Since both the

$x$ -coordinate and

$y$ -coordinate are negative, the point will lie in the

$III$ Quadrant.

State to which quadrant does the following points belong:
$C(8, 9)$

Since both the

$x$ -coordinate and

$y$ -coordinate are positive, the point will lie in the

$I$ Quadrant.

The $y$ -axis is the vertical number line.
enter 1 for true and 0 for false

True.

The y - axis is the vertical number line.

In which quadrant or on which axis will $(x, y)$ lie if $x<0$ and $y=0$ ?

We know, any point with coordinates in the form

$(x,0)$ , where

$x$ is any integer, lies on the x-axis.

Here, since

$x$ -coordinate is zero and

$x< 0$ .

Therefore, the point lies on negative

$x$ -axis.

For example, point

$A$ marked in the figure, satisfies the given condition and lies on the negative x-axis.

In which quadrant or on which axis will $(x, y)$ lie if $x=0$ and $y>0$ ?

We know, any point with coordinates in the form

$(0,y)$ , where

$y$ is any integer, lies on the y-axis.

Here, since

$x$ -coordinate is zero and

$y > 0$ .

Therefore, the point lies on positive

$y$ -axis.

For example, point

$A$ marked in the figure, satisfies the given condition and lies on the positive y-axis.

The origin $(0, 0)$ lies on the $x$ -axis.
Answer $1$ if True and $0$ if False.

We know, any point which lies on the

$x$ -axis will have coordinates of the form

$(x,0)$ , where

$x$ can be any real number.

The origin

$(0,0)$ is also of the form

$(x,0)$ , where

$x=0$ and therefore lies on the horizontal line which is the

$x$ -axis.

That is, the statement is true and

$1$ is the answer.

In which quadrant (in number) or on which axis will $(x, y)$ lie if $x<0$ and $y<0$ ?

We know,

Given, $x < 0, y < 0$ .

That is, $x$ is negative and $y$ is negative.

Hence, the given point $(x,y)$ lies in the $III$ rd quadrant.

Therefore, $3$ is the answer.

By using graph, the quadrant (in number) in which $(-2,5)$ lies is ____.

Given, $(-2,5)$ .

Here, the $x$ -axis is negative and $y$ -axis is positive.

Therefore, $(-2,5)$ lies in $2$ nd quadrant.

Hence, $2$ is the answer.

By using graph, (in numbers) find the quadrant or axis in which $(3,-2)$ lies.

Given, $(3,-2)$ .

Here, the $x$ -axis is positive and $y$ -axis is negative.

Therefore, $(3,-2)$ lies in $4$ th quadrant.

Hence, $4$ is the answer.

State true or false:
The origin is in the first quadrant.

We know, the origin is the point of intersection of the

$x$ -axis and the

$y$ -axis. That is, when

$x=0$ and

$y=0$ , we get the origin.

Then clearly, it does not lie in any of the quadrants.
Hence, the statement is false.

By using graph, the quadrant (in number) in which $(3,6)$ lies is ___ .

Given,

$(3,6)$ .

Here, both the

$x$ -axis and

$y$ -axis are positive.

Therefore,

$(3,6)$ lies in

$1$ st quadrant.

Hence,

$1$ is the answer.

Plot the following point on a graph paper: $(-4, -3)$ .

The required point is

$B$ is as shown in the graph.
1980177_197487_ans_9deaae271b764342acd3b358e857a4d2.png

If $(8, 7)$ is plotted in correct place of graph then write answer is $1,$ else $0$ .

Given,

$(8,7)$ .

Here, clearly both the

$x$ -axis and the

$y$ -axis are positive and lies in the

$I$ st quadrant.

Now, as shown in the graph,

$x$ and

$y$ coordinates

$(8,7)$ is plotted correctly in the

$I$ st quadrant.

Hence,

$1$ is the answer.

The point $(a, b)$ lies on the $y$ -axis if $b = 0$ .

We know, in the

$xy$ -plane, any point on the

$y$ -axis will have

$x =0$ .
Hence, any point on the

$y$ -axis is of the form

$(0,y)$ , where

$y$ can be any non-zero number.

Therefore, any point whose

$x$ -coordinate is

$0$ and

$y$ -coordinate is non-zero will lie on the

$y$ -axis.

But here, if

$b = 0$ in the point

$(a,b)$ , then it clearly lies on the

$x$ -axis.

That is, the statement is false.

Therefore,

$0$ is the answer.

If the ordinate of a point is equal to its abscissa; the point lies either in the first quadrant or in the second quadrant.

A point plotted on a graph has an abscissa or the

$x$ - coordinate

$(x)$ and the ordinate or the

$y$ - coordinate

$(y)$ .

If the ordinate of a point is equal to its abscissa; then both

$x$ and

$y$ are positive or negative. Hence, the point lies either in the first quadrant or in the third quadrant.

Therefore, the statement is false.

Hence,

$0$ is the answer.

The y-axis is the vertical number line.
If above statement is true then enter $1$ and if false then enter $0$ .

True.

In a graph, the y - axis is the vertical line on which we mark numbers ...-3, -2, -1, 0, 1, 2, 3... and so on. Hence, y - axis is the vertical number line.

The origin $(0, 0)$ lies on the $x$ -axis.

A point plotted on a graph has an abscissa or the

$x$ - coordinate

$(x)$ and the ordinate or the

$y$ - coordinate

$(y)$ .

An origin is formed by the intersection of the

$x$ and

$y$ axes. That is, when

$x=0$ and

$y=0$ . Hence, the coordinates of the origin is

$O(0,0)$ .

Then clearly, the origin lies on the

$x$ -axis.

Therefore, the statement is true.

Hence,

$1$ is the answer.

Every point is located in one of the four quadrants.

A point plotted on a graph has an x - coordinate (x) and the y - coordinate (y). It's position on the graph depends on the values of x and y. The point can lie in any of the four quadrants or on the x - axis or the y - axis.

If both x and y are zero, then the point lies at the intersection of the axes, and is called the Origin

$(0,0)$ .

Hence, it is not necessary for a point to lie in any of the four quadrants, as it can lie on the x-axis or the y - axis or it may be the origin.

How will you describe the position of a table lamp on your study table to another person?

The position of the table lamp is at a distance of a units from the left edge of the top of the table and at a distance

$b$ units above the bottom edge of the top of the table. We have marked the bottom edge as the line

$AX$ and the left edge as the line

$AY$ . Here

$AY \perp AX$ . We measure all distances along

$AX$ and

$AY$ from the corner

$A$ . The position of the lamp can be described as

$(a,b)$ .

The position of the lamp can be described as

$(a,b)$

Which of the following points lies on the x-axis
(i) $(1,1)$
(ii) $(1,0)$
(iii) $(0,1)$
(iv) $(0,0)$
(V) $(-1,0)$
(vi) $(0,-1)$
(vii) $(4,0)$
(viii) $(0,-7)$

Points of the form

$(a,0)$ , i.e. the points in which y - coordinate is 0, lie on the x-axis.

Hence, the points

$(1,0), (0,0) , (-1,0) , (4,0)$ lie on the x-axis.

Plot the points $(x,y)$ given in the following table on the plane, choosing suitable units of distance on the axes.
$x$ -2 -1 0 1 3
$y$ 8 7 -1.25 3 -1

Write the answer of each of the following questions:
$(i)$ What is the name of horizontal and the vertical lines drawn to determine the position of any point in the Cartesian plane?
$(ii)$ What is the name of each part of the plane formed by these two lines?
$(iii)$ Write the name of the point where these two lines intersect.

(i) The name of horizontal lines and vertical lines drawn to determine the position of any point in the Cartesian plane is

$x$ -axis and

$y$ -axis respectively.

(ii) The name of each part of the plane formed by these two lines

$x$ -axis and

$y$ -axis is quadrants.

(iii) The point where these two lines intersect is called origin.

In the diagram provided
If the coordinates of $B$ is $(k,-2)$ . Then the value of $k$ is

The perpendicular distance of

$B$ from

$y-axis$ is

$3$ and from

$x-axis$ is

$-2$ .

Hence, the required coordinate is

$B(3,-2)$ .

State the coordinates of S.

Coordinates of S are (1,4).

On the graph, plot the point $X (8, -3)$ .

Which of the points shown below lies in the 3rd quadrant?
A (-4, 2) B (4, 2) C (3, -5) D (-5, -2)

We know that,

In 1st quadrant the value of

$x$ and

$y$ are positive

In 2nd quadrant the value of

$x$ is negative and

$y$ is positive

In 3rd quadrant the value of both

$x$ and

$y$ are negative

In 4th quadrant the value of

$x$ is positive and

$y$ is negative

Thus,

$A(-4,2)$ is in 2nd quadrant

$B(4,2)$ is in 1st quadrant

$C(3,-5)$ is in 4th quadrant

$D (-5,-2)$ is in 3rd quadrant.

Ans:

$D(-5,-2)$

In the diagram, mark and label point $S (15, 4)$ .

The required point is $S$ is as shown in the graph.

1084028_516148_ans_60b9046e87dc46f4b9363baca301316f.png

On the graph, plot the point $V(-4, 10)$ .

State the coordinates of points $A, B, C$ and $D$ on the Cartesian plane below.

The coordinates of given points are:

$A(-6,10), B(2,20), C(4,-10)$ and

$D(-4,-15)$ .

Based on the graph, state the coordinates of the point U.

Coordinates of U are (-2,4)

Write the coordinates of points $A, B, C, D, E$ and $F$ on the Cartesian plane.

The coordinates of the given points are:

$A=(-2,1), B=(3,4),C=(1,-3), D=(-4,-2), E=(0,3)$ and

$F=(4,0)$ .

Fill in the blanks with suitable words:
The $y$ -coordinate of a point on the $x$ -axis is _____________.

Few examples of Points on

$x$ -axis are

$(1, 0) (2,0) (4,0)$

The general form of any point on the

$x$ -axis can be written as

$(a,0)$

So the

$y$ -coordinate of a point on the

$x$ -axis is 0

Find the quadrant in which $(8,-100)$ lie

We can see that the point

$(8,-100)$ lies in the fourth quadrant as abscissa of the point is a positive integer and ordinate of the point is a negative integer.

Find the quadrant in which $(-800,-3000)$ lie

We can see that the co-ordinate

$(-800,-3000)$ lies in the third quadrant as both abscissa and ordinate of the point are negative integers.

Find the quadrant in which the point $(5,10)$ lies in.

We can see that the co-ordinate

$(5,10)$ lies in the first quadrant as both abscissa and ordinate of the point are positive.

Find the quadrant in which $(-8,9)$ lie

We can see that the co-ordinate

$(-8,9)$ lies in the second quadrant as abscissa of the point is a negative integer and ordinate of the point is a positive integer.

Draw the graph of $\cfrac{y}{x}=\cfrac{y+1}{x+2}$

Given equation is

$\cfrac{y}{x}=\cfrac{y+1}{x+2}$

$\implies xy+2y=xy+x$

$\implies 2y=x$

Thus, the equation becomes

$y=\dfrac{1}{2}x$

We find some points for this equation

$x$

$0$

$2$

$-2$

$4$

$-4$

$6$

$-6$

$y$

$0$

$1$

$-1$

$2$

$-2$

$3$

$-3$

Plot these points on the graph and we get the graph shown above.

Suppose you are given a coordinate system. Determine the quadrant in which the following points lie:
$(i)$ $A(4,5)$ ; $(ii)$ $B(-4,-5)$ ; $(iii)$ $C(4,-5)$ .

As per the image,

$\text{I}^{st}$ quadrant has both the co-ordinates positive.

$\text{II}^{nd}$ quadrant has

$x$ co-ordinate negative and

$y$ co-ordinate positive.

$\text{III}^{rd}$ quadrant has both co-ordinates positive.

$\text{IV}^{th}$ quadrant has

$x$ co-ordinate positive and

$y$ co-ordinate negative.

$(i)$

$A(4,5)$ has both co-ordinate postive. So, it lies in first quadrant.

$(ii)$

$B(-4,-5)$ has both co-ordinates negative. So, it lies in third quadrant.

$(iii)$

$C(4,-5)$ has

$x$ positive and

$y$ negative. So, it lies in fourth quadrant.

Fill in the blanks with suitable words:
If a point $(x,y)\ne (0,0)$ is in the third quadrant, then $(x+y)$ has _________ sign.

If a point

$(x,y)$

$\neq (0,0)$ is in the third quadrant then

$(x+y)$ has negative sign

As in third quadrant both

$x$ any

$y$ are negative real numbers.

Fill in the blanks with suitable words:
The $x$ -axis and $y$ -axis intersect at ____________.

The x-axis and y-axis intersect at (0,0)

Write the coordinates of the points marked in graph.

(i) The point P is at a distance of +5 units from the X-axis and at a distance zero from the Y-axis. Therefore the x-coordinate of P is 0 and y-coordinate is 5. Hence the coordinates of P are

$(0, 5).$
So think & discuss that-
(ii) The coordinates of Q are

$(0, 3, 5),$
(iii) The coordinates of R are

$(0, 1),$
(iv) The coordinates of S are

$(0, -2),$
(v) The coordinates of T are

$(0, -5),$
Since every point on the Y-axis has no distance from the Y-axis, therefore the x-coordinate of the point lying on Y-axis is always zero. Y-axis is denoted by the equation x = 0.

Fill in the blanks with suitable words:
If a point $(x,y)$ lies above horizontal axis, then $y$ is always __________.

Let

$(x,y)$ be a point that always lies above the horizontal axis.

So, this means it lies above the

$x$ -axis.

There are

$2$ quadrants above

$x$ -axis that are

$I^{st}$ and

$II^{nd}$ quadrant.

In both quadrants, the value of the

$y$ -coordinate will be positive.

Hence, if a point

$(x,y)$ lies above the horizontal axis then

$y$ is always positive.

State True or False:
In a rectangular coordinate system, the coordinate axes are chosen such that they form a pair of perpendicular lines.

The coordinate axes divide the plane into four quadrant as shown in the above figure.

They cut at a point

$(0,0)$ called origin such that the four quadrants has a pair of co-ordinates with different signs.

For example, All the points in I

$^{st}$ quadrant has both the co-ordinates positive.

And as they intersect each other at origin, they form a pair of perpendicular lines.

Hence, the given statement is true.

Plot the following point in the Cartesian plane.
A(-5, -3)

Draw the X-axis(horizontal line) and Y-axis(vertical line).
Point A lies in the third quadrant because both x and y are negative. Start from zero, the Origin.
Move 5 units from zero to its left side that is along the negative part of the X-axis.
From there move 3 units along a line parallel to the negative part of the Y-axis i.e. downwards and mark it as point A.
1111008_571181_ans_902fcd1719e04ed088eed1277ffa95f2.PNG

1111008_571181_ans_902fcd1719e04ed088eed1277ffa95f2.PNG

Look at the graph. Write the coordinates of the points $A, B, C, D, E, F, G, H, I, J, K, L, L, M, N, P, O$ and $Q$ .

$A (-3,4)$	$G (3,-1)$	$M (-1,0)$
$B (0,5)$	$H (0.-1)$	$N (-1,3)$
$C (3,4)$	$I (-3,-1)$	$P (1,3)$
$D(2,4)$	$J (-3,0)$	$O(0,0)$
$E (2,0)$	$K (-2,0)$	$Q (1,0)$
$F (3,0)$	$L (-2,4)$

Write the following based on the graph.
The abscissa of N is

As we can see that point

$N$ lies on x axis, therefore the abscissa of point

$N$ will be

$4$

Name the quadrant on which following point lies:
$(4, -2)$

A point lies in the fourth quadrant if its abscissa is positive and ordinate is negative.

In the given point

$(4,-2)$ , value of abscissa is positive and value of ordinate is negative. Thus the given point lies in fourth quadrant.

1160922_571153_ans_ae16221ce04c4db9873760ed9efa8553.png

Plot the following point on the Cartesian plane.
$N(1, -6)$

1113890_571183_ans_825b90cf4eba46988316d210361a37a2.PNG

Write the following based on the graph.
The ordinate of Q is

It is clear from the dotted line that ordinate of point

$Q$ is

$7$

1076554_571160_ans_26f41114afc1403e8a3ce25d71aa9207.png

x 2 3 -1 0 -9 -4
y -3 -3 4 11 0 -6
Plot the following points in the Cartesian plane whose x, y coordinates are given.

(-3, 5), (-1, 7)

2150785_571198_ans_23a8352498cf4c20b7b41bc3e0b8ba8f.png

Join the following pairs of point by a straight line segment, in the graph:
(2, 5), (2, -4)

As shown in the graph points are plotted and line is joined
1121178_571207_ans_40887b7311c7469d984bcc117e7d846a.gif

(-3, -5), (2, -5)

2151432_571200_ans_2dee8e271b8a4316b0b4cad8e5786728.png

(-2, 1), (-2, 0)

1076976_571203_ans_d71ed36ebb7c4699b967f167eb625ec7.png

(4, -2), (4, -3)

1076767_571201_ans_56f9422bebef4920a0c8c71579883a2f.png

(-3, -4), (2, -4)

2151443_571199_ans_40695c6b1e144f8ab08a416377e6c62a.png

(-2, 4), (-2, 3)

1076769_571202_ans_1901ea1cec034627af7a568ce0ccf558.jpg

Join the following pairs of point by straight line segment, in the graph:
(-3, 2), (2, 2)

As shown in the graph points are plotted and line is joined
1121180_571214_ans_08b33811cd3d4cab9745969c378d9134.gif

Join the following pairs of point by straight line segment, in the graph:
(-3, 5), (-3, 4)

1349450_571206_ans_b9fe9aa12154428594462fb9d882f8cb.png

Join the following pairs of point by straight line segment, in the graph:
(2, -4), (4, -2)

1690868_571208_ans_e97c9da88bb34855a5d2430a2c8fd714.png

Draw the figure for an angle in the standard position. If the initial arm rotates through ${80}^{o}$ in the clockwise direction, then state the quadrant in which the terminal arm lies.

The terminal arm rotates in clockwise direction and the angle is

$-{80}^{o}$ .
The angle is between

$-{90}^{o}$ and

${0}^{o}$ .

$\therefore$ The terminal arm lies in the IV quadrant.

The terminal arm is in II (second) quadrant, what is the possible measure of an angle?

The terminal arm is in II quadrant.

So, the possible measure of an angle is between

${90}^{o}$ and

${180}^{o}$ or

$-{270}^{o}$ and

$-{180}^{o}$ .

For the angle in standard position if the initial arm rotates ${25}^{o}$ in anti-clockwise direction, then state the quadrant in which the terminal arm lies.

Since the arm rotates in anti-clockwise direction and the

$\angle$ is more than

${0}^{o}$ but less than

${90}^{o}$ .
The terminal arm lies in the 1st quadrant.

Draw the figure for an angle in the standard position. If the initial arm rotates through ${170}^{o}$ in the clockwise direction, then state the quadrant in which the terminal arm lies.

The terminal arm rotates in clockwise direction and the angle is

$-{170}^{o}$ .
The angle is between

$-{180}^{o}$ and

$-{90}^{o}$ .

$\therefore$ The terminal arm lies in the III quadrant.

Plot the following points on a graph paper and find out in which quadrant do they lie?
(i) A (3,5) (ii) B (-2 , 7) (iii) C (-3,-5) (iv) D (2, -7) (v) O (0, 0)

Draw the x and y axes. Mark the units along the x and y axes with a suitable scale.
(i) To plot the point A (3 , 5)
Here, the x-coordinate of A is 3 and the y-coordinate of A is 5. Both are positive. Hence the point A (3 , 5) lies in the quadrant I. Start at the Origin. Move three units to the right along the x-axis. Then turn and move 5 units up parallel to Y-axis and mark the point A (3 , 5).
(ii) To plot the point B (2 , 7)
Here, the x-coordinate of B is -2 which is negative and the y-coordinate of B is 7 which is positive. Hence the point B (-2 , 7) lies in the quadrant II. Start at the Origin. Move 2 units to the left along the x-axis. Then turn and move 7 units up parallel to y-axis and mark the point B (-2 , 7).
(iii) To plot the point C (-3 , -5) Here, the x-coordinate of C is -3 and the y-coordinate of C is -5. Both are negative. Hence the point C (-3 , -5) lies in the quadrant III. Start at the Origin. Move 3 units to the left along the x-axis. Then turn and move 5 units down parallel to y-axis. and mark the point C (-3, -5).
(iv) To plot the point D (2 , 7)
Here, the x-coordinate of the point D is 2 which is positive and the y-coordinate of D is -7 which is negative. Hence the point D (2 , -7) lies in the quadrant IV. Start at the Origin. Move 2 units to the right along the x-axis. Then turn and move 7 units down parallel to y-axis and mark the point D (2 , -7).
(v) To plot the point O (0, 0)
This is the origin. Both the x and y coordinates are zeros. It is the point of intersection of the axes x and y. Mark the point O (0,0).

Plot the point $(4, 5)$ on a graph sheet. Is it the same as $(5, 4)$ ?

Draw

$XOX'$ and

$YOY'$ and let them cut at the origin at

$O$ . Mark the units along the x-axis and y-axis with a suitable scale.
The given point is

$P (4, 5)$ .
Here the

$x-$ coordinate of

$P$ is

$4$ and the

$y-$ coordinate of

$P$ is

$5.$
And both are positive. Hence the point

$P (4, 5)$ , lies in the first quadrant.
To plot, start at the Origin

$O(0,0)$ . Move

$4$ units to the right along the

$x-axis$ . Then turn and move

$5$ units up parallel to

$y-axis$ . You will reach the point

$P (4, 5)$ . Then mark it. (As shown in the adjoining figure)
Next, let us plot the point

$Q (5, 4)$ . Here the x-coordinate of

$Q$ is

$5$ and the

$y-$ coordinate of

$Q$ is

$4$ . And both are positive. Hence, this point

$Q (5, 4)$ also lies in the quadrant

$I$ . To plot this point

$Q (5, 4)$ ; start at the Origin. Move

$5$ units to the right along the

$x-axis$ . Then turn and move

$4$ units up parallel to

$y-axis$ . You will reach the point

$Q (5, 4)$ . Then mark it (As shown in the above figure).

Draw the figure for an angle in the standard position. If the initial arm rotates through ${300}^{o}$ in the clockwise direction, then state the quadrant in which the terminal arm lies.

The terminal arm rotates in clockwise direction and the angle is

$-{300}^{o}$ .
The angle is between

$-{360}^{o}$ and

$-{270}^{o}$ .

$\therefore$ The terminal arm lies in the I quadrant.

Draw the line joining the following points.
P (-4,5) and Q (3,-4).

To draw the line joining the points P (-4 , 5) and Q (3 , -4)
First, plot the point (-4 , 5) and denote it by P. Next, plot the point (3 , -4) and denote it by Q.
Then, join the points P and Q. PQ is the required line.

Drawing straight parallel lines to axes :
Draw the graph of x = 0.

The equation x = 0 means; Whatever may be the y-coordinate, x-coordinate is always 0.

x	0	0
y	3	-3

Plot the points A (0 , 3) and B (0, 3).
Join the points A and B and extend this line to obtain the graph of x = 0.

$(-2, 8)$ point lies on ________ quadrant

In the given coordinates of point

$(-2,8)$ ,

$x$ -coordinate is negative and

$y$ -coordinate is positive.
Therefore the point lies in the second quadrant.

Identify the quadrants of the points $A(2, 3), B(-2, 3), C(-2, -3)$ and $D(2, -3)$ . Discuss the type of the diagram by joining all the points.

Point	A	B	C	D
Quadrant	I	II	III	IV

ABCD is a rectangle
1066469_620443_ans_de9b1486a52c4f008b25d8d8091e3779.jpg

Plot the following point in the rectangular coordinate system
$C(-2, -3)$

To plot

$(-2, -3)$ , draw a vertical line at

$x = - 2$ and draw a horizontal line at

$y = - 3$ .

The intersection of these two lines is the position of

$(-2, -3)$ in the Cartesian plane.

Thus, the point

$C(-2, -3)$ is located in the Cartesian plane.

1089111_620437_ans_d5e4c8c4130240c2a2a73b5cdf163615.png

Plot the following point in the rectangular coordinate system.
$D(3, - 2)$

To plot

$(3, - 2)$ , draw a vertical line at

$x = 3$ and draw a horizontal line at

$y = -2$ .

The intersection of these two lines is the position of

$(3, - 2)$ in the Cartesian plane.

Thus, the point

$D(3, -2)$ is located in the Cartesian plane.

1089117_620438_ans_0ca3a0c031df45e88587436f8931378e.png

Plot the following point in the rectangular coordinate system.
$B(-4, 3)$

To plot

$(-4, 3)$ , draw a vertical line at

$x = - 4$ and draw a horizontal line at

$y = 3$ .

The intersection of these two lines is the position of

$(-4, 3)$ in the Cartesian plane.

Thus, the point

$B(-4, 3)$ is located in the Cartesian plane.

1089110_620436_ans_196098e7133341a48441fc0707a6405f.png

Plot the following point in the rectangular coordinate system.
$A(5, 4)$

To plot

$(5, 4)$ , draw a vertical line at

$x = 5$ and draw a horizontal line at

$y = 4$ .

The intersection of these two lines is the position of

$(5, 4)$ in the cartesian plane.

Thus, the point

$A(5, 4)$ is located in the cartesian plane.

1089105_620435_ans_be7904ec2d864ae895ae2fe5d7d2d45b.png

Plot the points $(0, 4), (0, - 2), (0, 5)$ and $(0, -4)$ in the cartesian plane.

$\textbf{Step 1: Plot points on a Cartesian plane by looking at x and y coordinate of point.}$

$\text{Given, Points has x coordinate equal to 0}$

$\therefore \text{Points lies on y-axis}$

$\textbf{Hence, all the given points lie on y-axis.}$

Plot the points $(-1, 0), (2, 0), (-5, 0)$ and $(4, 0)$ in the cartesian plane.

$\textbf{Step 1: Plot points on a Cartesian plane by looking at x and y coordinate of the point.}$

$\text{Given, points (−1,0),(2,0),(−5,0) and (4,0)has y coordinate equal to 0}$

$\therefore \text{Points lies on x-axis}$

$\textbf{Hence, Points lies on x-axis.}$

Determine the quadrants and the coordinates of the points A, B, C, D, E, F, G, H and O in the given figure.

$\Rightarrow$ (0,4) : Y-axis

$\Rightarrow$ (-3,2) :

$II$ Quadrant

$\Rightarrow$ (-5,0) : X-axis

$\Rightarrow$ (-4,-6) :

$III$ quadrant

$\Rightarrow$ (0,-3) : Y-axis

$\Rightarrow$ (7,-1) :

$IV$ Quadrant

$\Rightarrow$ (4,0) : x-axis

$\Rightarrow$ (6,3) :

$I$ Quadrant

$\Rightarrow$ (0,0) : Origin

Plot the points (i) $(-1, 2)$ , (ii) $(-4, 2)$ , (iii) $(4, 2)$ and (iv) $(0, 2)$ . What can you say about the position of these points?

When you join these points, you see that they lie on a line which is parallel to x-asix.
1066465_620442_ans_92e5384a725f43e28ec8742ac406e9dc.jpg

Write down the abscissa for the following point.
$(3, 5)$

Abscissa is the

$x–coordinate$ of any point

$A(x, y)$ .

So,abscissa of point

$(3, 5)$ is

$3$ .

1348894_620476_ans_994ad468b80c4b58a300a64e75859894.png

On which axis do the following points lie?

(i) $P(5,0)$ (ii) $Q(0.-2)$ (iii) $R(-4,0)$ (iv) $S(0,5)$

If the point lies on the x-axis, y co-ordinate =0

If the point lies on the y-axis, x co-ordinate =0

$P(5,0)$ y co-ordinate=0, so the point lies on x-axis

$Q(0,-2)$ x co-ordinate=0, so the point lies on y-axis

$R(-4,0)$ y co-ordinate=0, so the point lies on x-axis

$S(0,5)$ x co-ordinate=0, so the point lies on y-axis

Plot the following points. $A(0, 4), B(2, 3), C(1, 1)$ and $D(2, 0)$ .

Graph is presented in the figure

What is meant by positive direction of x axis or y axis given in question.

The coordinates are divided into for quadrants as shown in the diagram,

The positive direction of x-axis or y-axis means the positive values of the

$x,y$ coordinates

1113896_709451_ans_84fc374c62024562bd2bc34347af135f.png

Write down the ordinate of the following point.
$(-5, 8)$

Ordinate is the

$y–coordinate$ of any point

$A(x, y)$ .

So, ordinate of point

$(–5, 8)$ is

$8$ .

1348903_620482_ans_8ebaf7acc0294a789a36c9d04bd6f154.png

Write down the ordinate of the following point:
$(7, 5)$

Ordinate is the

$y–coordinate$ of any point

$A(x, y)$ .

So, ordinate of point

$(7, 5)$ is

$5$ .

1348899_620480_ans_6028a6e16a7445f4aa5993a497e3e75d.png

Write down the ordinate of the following point.
$(2, 9)$

Ordinate is the

$y–coordinate$ of any point

$A(x, y)$ .

So, ordinate of point

$(2, 9)$ is

$9$ .

1348902_620481_ans_ab090388e19b434596b8c076df830eb9.png

Draw the $x$ and $y$ axes and mark the points $(0, 4), (2, 5)$ and $(-3, -2).$

If the abscissa of any point is Zero then that point will lie on _________.

$y-axis$

In which quadrant or on which axis each of the following point lie? $(-3, 5), (2, 0), (-3, -5), (4, -1)$

In the first quadrant,

$x$ and

$y$ -coordinate of a point are positive.

In the second quadrant,

$x$ -coordinate is negative and

$y$ -coordinate

is positive. So,

$(-3,5)$ lies in second quadrant.

In the third quadrant,

$x$ and

$y$ -coordinate are negative. So,

$(-3,-5)$ lies in the third quadrant.

In the fourth quadrant,

$x$ -coordinate is positive and

$y$ -coordinate

is negative. So,

$(4,-1)$ lies in fourth quadrant.

Any point on the

$x$ -axis have the value of

$y$ -coordinate

$=0$

So,

$(2,0)$ lies on the

$x$ -axis.

Plot the following points on the same graph.
$(8, 7)$
$(3, 6)$
$(0, 4)$
$(0, -4)$
$(3, -2)$
$(-2, 5)$
$(-3, 0)$
$(5, 0)$
$(-4, -3)$

977430_1052002_ans_6e518d414fe9405bb9b99d94023fd3b9.png

Plot on graph $p(-5, 7)$
$Q(-1, 3)$

In the above figure the given point are indicated
1161729_1053547_ans_4c9eece857484e82bcb6b66c69dbae9a.PNG

Find the co-ordinates of the point which lies on both X and Y-axis.

1315383_1062924_ans_abe3d3032b9f4457875fa2ee55f0758a.jpg

Name the axis of quadrant on which the point $(3, 0)$ lies.

$x=3$ in frist quardent.

Hence, this is the answer.

What is the distance of point $(3, 2)$ from x-axis?

$\textbf{Step-1: Apply the distance formula to get the required unknown.}$

$\text{Point}$

$(a,b)$

$\text{lies at distance of}$

$b$

$\text{from}$

$\text{x- axis and}$

$a$

$\text{from}$

$\text{y-axis.}$

$\text{Given point is}$

$(3,2)$

$\text{It can be seen in the figure.}$

$\text{Distance from}$

$\text{x-axis}$

$\text{= y-ordinate}$

$=2 \ units$

$\text{In case of negative values of}$

$\text{y-coordinates, only absolute values should be taken.}$

$\textbf{Hence, answer is 2 units.}$

2178858_1025788_ans_3d3682e8cfb444ca91f5e2603dabaa18.png

Plot the following points in the Cartesian plane whose x,y co-ordinates are given.
x 2 3 -1 0 -9 -4
y -3 -3 4 11 0 -6
(x,y)

X=2 3 -1 0 -9 -4

Y = -3 -3 4 11 0 -6

(x,y) = A B C D E F

1114811_1078341_ans_ab044c886eb04e139e89366a5d79f571.JPG

Plot the following points on a Graph paper join the line and identify the figure:
a) A(2,5), B(2, 7), C(4, 7) D(4, 3)
b) J(4, 3) K(10, 3) L(9, 7) M(5, 7)

a)By plotting, we observe that

$AB$ is parallel to

$CD$ and

$AD\neq BC$ (also not parallel). Hence

$ABCD$ is a trapezium.
b)a)By plotting, we observe that

$ML$ is parallel to

$JK$ and

$MJ$ is not parallel to

$LK$ . Hence

$JKLM$ is a trapezium.
1320819_1053693_ans_85ae2f3204904495be6aae5249f4c9c3.png

Mark the following points on quadrant or axis:
$A(2 ,-3) ; B(4 , 1) ; C(-5 , -3/2) ; D(3 , 0) , E(-3 , 4) , F(0 , -5) , G(-1 , 0) , H(3 , 3)$ .

1317780_1056653_ans_814d2549c983422bb2169497fb1ff115.png

In which quadrant or axis are on which axis do each of the points $(-2,4),(3,-1),(-1,1),(1,2)$ lie?

$(-2,4)$ - lies on II quadrant

$(3,-1)$ - lies on IV quadrant

$(-1,1)$ -lies on II quadrant

$(1,2)$ -lies on I quadrant

plot the following points on a Graph paper join the line and identify the figure:
a) A(2,5), B(2, 7), C(4, 7) D(4, 3)
b) J(4, 3) K(10, 3) L(9, 7) M(5, 7)

By plotting, we know, both ABCD and JKLM are trapezium.
1281355_1351737_ans_a12c25ce6cb8457aae533ff36c2375e6.jpg

State the quadrants in which the following point lie.
(i) $A\left(-5,-3\right)$
(ii) $B\left(3,-\dfrac {5}{2}\right)$

$(1)$ is Fourth quadrants and

$(2)$ is Third quadrants.

To which quadrant do the following points belong ?
$(5, 7)$
$(-5, -7)$
$(-5, 7)$
$(5, -7)$

$A = (5, 7) \in Q_1$

$B = (-5, -7) \in Q_3$

$C = (-5, 7) \in Q_2$

$D = (5, -7) \in Q_4$

In which quadrant will the point lie if the ordinate is $3$ units and the abscissa is $4$ units.

Abscissa

$=$ x coordinate

$= 4$

Ordinate

$=$ y coordinate

$= 3$

The point will lie in the

$1^{st}$ quadrant.

1187805_1353242_ans_95e6a982a9874fba9c431564bf8b2766.jpg

In which quadrant do the points $(-2, 4)$ and $(3, -1)$ lie?

$x$ axis is negative and

$y$ axis is positive in point

$(-2,4)$ so its lies in

$2^{nd}$ quadrant.

$y$ axis is negative and

$x$ axis is positive in point

$(3,-1)$ so its lies in

$4^{th}$ quadrant.

Find the perpendicular distance between $(3,4)$ from $x$ and $y$ axis.

Given point is

$(3,4)$

$x-coordinate=3$

$y-coordinate=4$

Perpendicular distance from

$x$ axis

$=y-coordinate=4$

Perpendicular distance from

$y$ axis

$=x-coordinate=3$

When any of the coordinates are negative, only their absolute value is considered.

In which quadrant or on which axis each of the $(2,3) ,(0,2)$ lies ?

If the

$x-$ coordinate and

$y-$ coordinate are positive, the points lies

$1st$ quadrant.

$\therefore\,\left(2,3\right)$ lies in first quadrant and the point

$\left(0,2\right)$ lies on

$y-$ axis since

$x=0$

If a line is passing through the points $(2, -5), (-5, -5)$ then prove that line will be parallel to $x$ axis and if a line is passing through the points $(6, 3), (6, -3)$ then prove that line will be perpendicular to the $x$ -axis.

Slope of line passing through

(2, -5) and (-5, -5) is

$\Rightarrow$ line is 11 to x- axis

slope of line passing through

(6,3), (6,-3) is

$\infty$

$\Rightarrow$ line is parallel to y-axis

1120184_1202010_ans_630edb38301542eb8ee725b2dbf5fbd1.jpg

Write the quadrants:
$A(4,3),B(3,4),C(2,5),D(-2,4)E(1,-3),F(-5,-4),G(-2,0),H(-2,-1),L(0,4),M(5,0)$

First quadrant	$A\left(4,3\right),B\left(3,4\right),C\left(2,5\right)$
Second quadrant	$D\left(-2,4\right),\left(-2,0\right)$
Third quadrant	$F\left(-5,-4\right),H\left(-2,-1\right)$
Fourth quadrant	$E\left(1,-3\right)$

Plot the following points on the graph paper: $\left ( 7, -4\right )$

Here the

$\text{x-coordinate}$ of our point is

$7$ and the

$\text{y-coordinate}$ of our point is

$-4$

As the

$\text{x-coordinate}$ is positive and

$\text{y-coordinate}$ is negative ,Point

$(7,-4)$ lies in Fourth Quadrant

To plot the point ,start at the origin .Move seven units to the right along the

$x-$ axis. Then turn and move four units down parallel to

$\text{y-axis}$ and mark the point as

$(7,-4)$

1653310_1669179_ans_a19bb591ca354741be4037b2369f254e.png

The position of $(3, 4)$ and $(4, 3)$ are not the same on graph. Why?

In graph, points are same only if their corresponding values of

$x$ and

$y$ co-ordinate are same. In the given points values of corresponding co-ordinates are not same. Hence the given points are not same

$A(1, -2), B(0, 4), C(-3, 0), D(-2, -1), E\left(\dfrac{3}{4}, -8\right), F\left(-4, \dfrac{3}{4}\right)$ are six points Cartesian plane. Then in which quadrant does point $C$ lie?

$C$ has x coordinates negative and y-coordinate

$O\Rightarrow C$ lie on negative x-axis (Boundary of quadrant II, III)
1226919_1398285_ans_a2a01f5e419947f59dd9e9544ad117bf.jpg

In which quadrant will the point lie if the ordinate is $3$ and the abscissa is $-2$ .

According to the problem, the point is

$(-2,3)$ so the point lies in the II quadrant as it has negative

$X$ and positive

$Y$ .

Plot the following points on the graph paper: $\left ( 4,-3 \right )$

Here the

$\text{x-coordinate}$ of our point is

$4$ and the

$\text{y-coordinate}$ of our point is

$-3$

As the

$\text{x-coordinate}$ is positive and

$\text{y-coordinate}$ is negative ,Point

$(4,-3)$ lies in Fourth Quadrant

To plot the point ,start at the origin .Move four units to the right along the

$x-$ axis. Then turn and move three units down parallel to

$\text{y-axis}$ and mark the point as

$(4,-3)$

1653294_1669174_ans_8f1e741146564a438174a9149b1ff117.png

Plot the following points on the graph paper: $\left ( 2,5 \right )$

Here the

$\text{x-coordinate}$ of our point is

$2$ and the

$\text{y-coordinate}$ of our point is

$5$

As the both coordinates are positive ,Point

$(2,5)$ lies in First Quadrant

To plot the point ,start at the origin .Move two units to the right along the

$x-$ axis. Then turn and move five units up parallel to

$\text{y-axis}$ and mark the point as

$(2,5)$

1653269_1669172_ans_00bf61a2146447ad993ca3ea764da85f.png

Plot the following points on the graph paper: $\left ( -3, 2 \right )$

Here the

$\text{x-coordinate}$ of the point is

$-3$ and the

$\text{y-coordinate}$ of the point is

$2$

As the

$\text{x-coordinate}$ is negative and

$\text{y-coordinate}$ is positive, point

$(-3,2)$ lies in Second Quadrant

To plot the point, start at the origin. Move three units to the left along the

$\text{x-axis}$ . Then turn and move two units up parallel to

$\text{y-axis}$ and mark the point as

$(-3,2)$ .

1653333_1669182_ans_6e8acd509dd84b0daec5d07ee852a387.png

State the quadrant in which each of the following points lies:-
$(2,-3),(-8,-10),(4,5),(-6,-2),(3,2),(3,-2),(-4,3)$

First quadrant	$\left(4,5\right),\,\left(3,2\right)$
Second quadrant	$\left(-4,3\right)$
Third quadrant	$\left(-8,-10\right),\,\,\left(-6,-2\right)$
Fourth quadrant	$\left(2,-3\right),\left(3,-2\right)$

1336032_1383843_ans_e52b95645cbe45f5947f5dffa7e17be2.png

Plot the following points on the graph paper: $\left ( -5, -7 \right )$

Here the

$\text{x-coordinate}$ of our point is

$-5$ and the

$\text{y-coordinate}$ of our point is

$-7.$

As the

$\text{x-coordinate}$ is negative and

$\text{y-coordinate}$ is negative ,Point

$(-5,-7)$ lies in Third Quadrant.

To plot the point, start at the origin. Move five units to the left along the

$x-$ axis. Then turn and move seven units down parallel to

$\text{y-axis}$ and mark the point as

$(-5,-7).$

1653323_1669176_ans_953e1721161f4919954ac16e44ebe722.png

For the following point, write the quadrant in which it lies:
$\displaystyle (11, 6)$

The given point is

$\displaystyle (11, 6)$

$\displaystyle 11$ is the

$x$ -coordinate of the point, and it is positive.

$\displaystyle 6$ is the

$y$ -coordinate of the point, and it is also positive.

Therefore,

$\displaystyle (11, 6)$ lies in

$Quadrant-I$ .

Plot the following point on the graph paper: $\left ( 0, 7 \right )$

REF Image.

In the image, the vertical line is Y-axis and the horizontal line is X-axis.

Here the

$\text{x-coordinate}$ of our point is

$0$ and the

$\text{y-coordinate}$ of our point is

$7$

As the

$\text{x-coordinate}$ is zero and

$\text{y-coordinate}$ is positive, Point

$(0,7)$ lies on positive

$\text{y-axis}$

To plot the point, start at the origin. Move

$7$ units up along the

$y-$ axis and mark the point as

$(0,7)$ .

1653369_1669191_ans_4a7548ccf23d42c09b416c314403a484.png

For the following points, write the quadrant in which it lies. $\displaystyle (1, -4)$

In the given point

$\displaystyle (1, -4)$

$x$ -coordinate

$1$ is positive and

$y$ -coordinate

$-4$ is negative.

Therefore,

$\displaystyle (1, -4)$ lies in the

$\displaystyle IV$ quadrant.

Plot the following point on the graph paper: $\left ( 0, -4 \right )$

Here the

$\text{x-coordinate}$ of the point is

$0$ and the

$\text{y-coordinate}$ of the point is

$-4$

As the

$\text{x-coordinate}$ is zero and

$\text{y-coordinate}$ is negative ,point

$(0,-4)$ lies on negative

$\text{y-axis}$

To plot the point ,start at the origin .Move

$4$ units down along the

$y-$ axis and mark the point as

$(0,-4)$

1653376_1669194_ans_3d0cff8e89a64cc9a752130031aa0472.png

On the plane of a graph paper draw $\displaystyle X’OX$ and $\displaystyle YOY’$ as coordinate axes and plot each of the following points.
$\displaystyle (i) \ \ \ \ A (5, 3)$
$\displaystyle (ii) \ \ \ \  B (6, 2)$
$\displaystyle (iii) \ \ \ \  C (-5, 3)$
$\displaystyle (iv) \ \ \ \  D (4, -6)$
$\displaystyle (v) \ \ \ \  E (-3, -2)$
$\displaystyle (vi) \ \ \ \  F (-4, 4)$
$\displaystyle (vii) \ \ \ \  G (3, -4)$
$\displaystyle (viii) \ \ \ \  H (5, 0)$
$\displaystyle (ix) \ \ \ \  I (0, 6)$
$\displaystyle (x) \ \ \ \  J (-3, 0)$
$\displaystyle (xi) \ \ \ \  K (0, -2)$

1565092_1715309_ans_6320c83c8af34b70bf609624c8a84f5c.png

Plot the following point on the graph paper: $\left ( -4, 0 \right )$

Here the

$\text{x-coordinate}$ of our point is

$-4$ and the

$\text{y-coordinate}$ of our point is

$0$

As the

$\text{x-coordinate}$ is negative and

$\text{y-coordinate}$ is zero ,Point

$(-4,0)$ lies on negative

$\text{x-axis}$

To plot the point ,start at the origin .Move

$4$ units to the left along the

$x-$ axis and mark the point as

$(-4,0)$

1653356_1669187_ans_023e9c4674e54f6db92b3656cd984f7d.png

Plot the following points on the graph paper: $\left ( 0, 0 \right )$

REF Image: The vertical line is

$y-axis$ and horizontal line is

$x-axis$ .

Here the

$\text{x-coordinate}$ of our point is

$0$ and the

$\text{y-coordinate}$ of our point is

$0$

As the

$\text{x-coordinate}$ is zero and

$\text{y-coordinate}$ is zero ,Point

$(0,0)$ is the origin

Origin is the point where

$\text{x-axis}$ and

$\text{y-axis}$ meets each other, Mark that point as

$(0,0)$

1653389_1669198_ans_082fb5fa1dc7418a8728e98f9616861d.png

Plot the following points on the graph paper: $\left ( 7, 0 \right )$

Here the

$\text{x-coordinate}$ of our point is

$7$ and the

$\text{y-coordinate}$ of our point is

$0$

As the

$\text{x-coordinate}$ is positive and

$\text{y-coordinate}$ is zero ,Point

$(7,0)$ lies on positive

$\text{x-axis}$

To plot the point ,start at the origin .Move

$7$ units to the right along the

$x-$ axis and mark the point as

$(7,0)$

1653350_1669184_ans_cf8ffe3f6d284494bbe181519c6d657a.png

For the following points, write the quadrant in which it lies. $\displaystyle (-6, 3)$

Quadrant	Sign of $x$ coordinate	Sign of $y$ coordinate
$I$	+	+
$II$	-	+
$III$	-	-
$IV$	+	-

For the coordinate

$\displaystyle (-6, 3)$

The

$x$ coordinate is negative and the

$y$ coordinate is positive.

Therefore,

$\displaystyle(-6, 3)$ lies in the

$\displaystyle II$ quadrant.

For the following points, write the quadrant in which it lies. $\displaystyle (-5, -3)$

For the coordinate

$\displaystyle (-5, -3);$

$\displaystyle -5$ which is the x-coordinate is negative and

$\displaystyle -3$ which is the y-coordinate is negative.

Therefore,

$\displaystyle (-5, -3)$ lies in the

$\displaystyle III$ quadrant since both the coordinates are negative.

Write the axis on which the given point lies: $\displaystyle (0, -1)$

Since the point

$\displaystyle (0, -1)$ is of the form

$\displaystyle (0, y)$ it lies on the

$y-axis$ .

Write the axis on which the given point lies. $\displaystyle (2, 0)$

The given point is

$(2, 0)$

To find out: On which axis does the point lie?

We know that, the

$x-coordinate$ of a point is the perpendicular distance of the point from

$y-axis$ and the

$y-coordinate$ is the perpendicular distance from the

$x-axis$ .

Since, the

$y-coordinate$ of the given point is

$0$ , it is at a

$0$ distance from the

$x-axis$ .

Hence, it lies on the

$x-axis$

Therefore,

$(2, 0)$ lies on the

$x-axis$ .

For the following points, write the quadrant in which it lies. $\displaystyle (-3, 8)$

For the coordinate

$\displaystyle (-3, 8)$

$\displaystyle -3$ which is the x-coordinate is negative and

$\displaystyle 8$ which is the y-coordinate is positive.

Therefore,

$\displaystyle (-3, 8)$ lies in the

$\displaystyle II$ quadrant.

Write the axis on which the given point lies. $\displaystyle (0, -5)$

Given point is

$(0,-5)$

We know that the x-coordinate of a point is the perpendicular distance of the point from

$y-axis$ and the y-coordinate is the perpendicular distance of the point from

$x-axis$ .

We can see that the x-coordinate of the given point is

$0$ .

Hence, the point is at

$0$ perpendicular distance from

$y-axis$ .

Therefore, the point

$(0,-5)$ lies on the

$y-axis$

Write the axis on which the given point lies. $\displaystyle (-4, 0)$

$X$ -axis, y-coordinate of point is

$0$ .

Since the point

$\displaystyle (-4, 0)$ is of the form

$\displaystyle (x, 0)$ it lies on the

$x-axis$ .

Which of the following points lie on the x-axis?
$\displaystyle (i) A (0, 8)$
$\displaystyle (ii) B (4, 0)$
$\displaystyle (iii) C (0, -3)$
$\displaystyle (iv) D (-6, 0)$
$\displaystyle (v) \ \ E (2, 1)$
$\displaystyle (vi) F (-2, -1)$
$\displaystyle (vii) G (-1, 0)$
$\displaystyle (viii) H (0, -2)$

The points which lie on the x-axis are of the form

$\displaystyle (x, 0)$

Therefore, the points which lie on the x-axis are

$\displaystyle B (4, 0), D (-6, 0)$ and

$\displaystyle G (-1, 0)$ .

We need ________ coordinates for representing a point on the graph sheet.

We need two(x &y) coordinates for representing a point on the graph sheet.

For the following points, write the quadrant in which it lies. $\displaystyle (-7, -4)$

For the coordinate

$\displaystyle (-7, -4)$

$\displaystyle -7$ which is the x-coordinate is negative and

$\displaystyle -4$ which is the y-coordinate is negative.

Therefore,

$\displaystyle (-7, -4)$ lies in the

$\displaystyle III$ quadrant.

For the following point, write the quadrant in which it lies.
$\displaystyle (4, -1)$

For the coordinate

$\displaystyle (4, -1)$

$\displaystyle 4$ which is the x-coordinate, is positive and

$\displaystyle -1$ which is the y-coordinate, is negative.
We know that for a point when

$x$ is positive and

$y$ is negative then it lies in the 4th quadrant.

Therefore,

$\displaystyle (4, -1)$ lies in the

$\displaystyle IV$ quadrant.

From the given graph, choose the letters that indicate the location of the point given below.
$(3, 3)$

According to the given graph.

E is the point that represents the position of the point

$(3, 3)$ . For the given point, the x-coordinate is

$3$ and y-coordinate is

$3$ .

Which of the following points lie on y - axis ?
$A \left(1,1\right), B \left(1,0\right), C \left(0,1\right), D \left(0, 0\right), E \left(0,-1\right), F \left(-1,0\right), G \left(0,5\right), H \left(-7,0\right),I \left(3,3\right)$ .

We know that if a point lies on the y - axis, its abscissa is

00 are the points which lie on y - axis.

Plot the following points and write the name of the figure obtained by joining them in order :
$P \left(-3,2\right), Q \left(-7,-3\right), R \left(6,-3\right), S\left(2,2\right)$

Let

$X'OX$ an d

$Y'OY$ be the coordinate axes. Then, the four points may be plotted as given below :

Let X’ OX and Y’ OY be the coordinate axes and mark point on it.

Here, point P(-3,2) lies in II quadrant, Q(-7,-3) lies in III quadrant, R(6, -3) lies in IV quadrant and S(2,2) lies in I quadrant. Plotting the points on the graph paper, the figure obtained is trapezium PQRS.

1659780_1794409_ans_6794a717e2474ad09d053a223f504e7e.png

In which quadrant or on which axis each of the following points lie ?
$\left(-3,5\right), \left(4,-1\right), \left(2,0\right),\left(2,2\right), \left(-3,-6\right)$

(i) In point

$\left(-3,5\right)$ , x - coordinate is negative and y - coordinate is positive, so it lies in

$II$ quadrant.
(ii) In point

$\left(4,-1\right)$ , x - coordinate is positive and y - coordinate is negative, so it lies in

$IV$ quadrant.
(iii) In point

$\left(2,0\right)$ , x - coordinate is positive and y - coordinate is zero, so it lies on X - axis.
(iv) In point

$\left(2,2\right)$ , x-coordinate and y - coordinate both are positive, so its lies in

$I$ quadrant.
(v) In point

$\left(-3,-6\right)$ , x - coordinate and y - coordinate both are negative, so its lies in

$III$ quadrant.

Without plotting the points indicate the quadrant in which they will lie, if
(i) ordinate is $5$ and abscissa is $-3$
(ii) abscissa is $-5$ and ordinate is $-3$
(iii) abscissa is $-5$ and ordinate is $3$
(iv) ordinate is $5$ and abscissa is $3$

(i) In the point

$\left(-3,5\right)$ abscissa is negative and ordinate is positive, so it lies in the second quadrant.

(ii) In the point

$\left(-5, -3\right)$ abscissa and ordinate both are negative, so it lies in the third quadrant.

(iii) In the point

$\left(-5,3\right)$ abscissa is negative and ordinate is positive, so it lies in the second quadrant.

(iv) In the point

$\left(3,5\right)$ abscissa and ordinate both are positive, so it lies in the first quadrant,

Plot the points $\left(x,y\right)$ given by the following table. Use scale $1\, cm = 0.25\, units$
x 1.25 0.25 15 -1.75
y -0.5 1 1.5 -0.25

Let

$X'OX$ and

$Y'OY$ be the coordinates axes. Then, the given points may be plotted as given below :
1659872_1794495_ans_5e0a78975f2844269efa257e87a21a81.png

In Fig.3.6, LM is a line parallel to the y - axis at a distance of $3$ units.
(i) What are the coordinates of the points P,R and Q ?
(ii) What is the difference between the abscissa of the points L and M ?

Given LM is a line parallel to the Y - axis and its perpendicular distance from Y - axis is

$3$ units
(i) Coordinates of point

$P = \left(3,2\right)$

$\left[Since, \, its\, perpendicular \, distance\, from\, X - axis\, is \,2\right]$
Coordinate of point

$Q = \left(3,-1\right)$

$\left[Since, \, its\, perpendicular \, distance\, from\, X - axis\, is \,1\,in \,negative\,direction\, of \, Y- axis\right]$ . Coordinate of point

$R = \left(3,0\right)$ [since its lies on X - axis, so its y-coordinate is zero.]
(ii) Abscissa of point

$L = 3$ , abscissa of point

$M = 3$

$\therefore$ Difference between the abscissa of the points L and M

$= 3 - 3 = 0$

Plot the points $\left(x,y\right)$ given by the following table :
X 2 4 -3 -2 3 0
Y 4 2 0 5 -3 0

Let

$X'OX$ and

$Y'OY$ be horizontal and vertical coordinate axes. Then, the given points may be plotted as shown above.
1659791_1794419_ans_97dcbccab95d4793a114e6be6fbb3a35.png

1659791_1794419_ans_97dcbccab95d4793a114e6be6fbb3a35.png

In which quadrant are the following points ?
Whose both co - ordinate are positive .

The x co - ordinate and y co - ordinate of a point are both are positive in the first quadrant.

In the given figure, LM is a line parallel to the y-axis at a distance of 3 units. What is the difference between the abscissa of the points L and M?

Any point on a line parallel to the

$y$ -axis and at a distance

$a$ , will have the co-ordinates

$P(x,y)=(a,y).$

i.e

$y$ may take any value but

$x$ remains constant which is

$a$ .

So, the difference between the abscissae of any two points is

$a-a=0.$

Here,

$a=3$ units.

The ordinate of

$L$ is

$4\longrightarrow$ the co-ordinates are

$L(3,4)$ .

Similarly, the ordinate of

$M$ is

$-3\longrightarrow$ the co-ordinates are

$M(3,-3).$

$\therefore$ The difference of the abscissae of

$L$ &

$M$ is

$3-3=0$ .

Hence, the required answer is

$0$ .

Mark and label point $B$ is $(-3, 2)$ .
If true enter $1$ , else $0$ .

Let the given point be,

$A(-3,2)$ .

Here, the

$x$ -coordinate is

$-3$ and negative.

Also, the

$y$ -coordinate is

$2$ and positive.

Hence, the point lies in the

$II$ nd quadrant.

and can be plotted as shown.

But in the figure, the point is plotted in the

$IV$ th quadrant and the point is

$B(3,-2)$ .

Therefore, the statement is false and

$0$ is the answer.

1170435_106071_ans_bf3b1b8aa59e4ddb9f7ffd337feeae93.png

The coordinates of $B$ is $(3,-2)$ .
If true, enter $1$ or else $0$ .

Let the given point be,

$A(3,-2)$ .

Here, the

$x$ -coordinate is

$3$ and positive.

Also, the

$y$ -coordinate is

$-2$ and negative.

Hence, the point lies in the

$IV$ th quadrant.

In the figure, the point is plotted in the

$IV$ th quadrant and the point is

$B(3,-2)$ .

Hence, the statement is true and

$1$ is the answer.

With reference to figure, see which quadrants or axes do the points L, M, N, K, G, B, R, T and D belong, and find the sum of the abscissa of all the marked points.

Concept: for any point P(m,n), m is called abscissa and n is called ordinate.

Point	Position
L(3, 2)	I quadrant
M(-3, 1)	II quadrant
N(-4, -2)	III quadrant
K(4, 0)	X-axis
G(-1, 0)	X-axis
B(0, 3)	Y-axis
R(2, -1)	IV quadrant
T(5, -2)	IV quadrant
D(0, -2)	Y-axis

sum of abscissa of all points

$= 3 + (-3) + (-4) + (-1) + 0 + 2 + 5 + 0\\ = 3 -3 -4 -1 +2 +5 \\= 2$

Plot the point $(0,2)$ on a graph paper.

In the given point $(0,2)$ ,

the x-coordinate is zero and the y-coordinate is positive.

Therefore, it lies on the positive $y$ -axis as shown in the graph.

Plot the point $(-5,4)$ on a graph paper.

In the given point

$(-5,4)$ ,

the x-coordinate is negative and the y-coordinate is positive.

Therefore, it lies in the

$II$ nd quadrant as shown in the graph.

Plot the point $(-3,-4)$ on a graph paper.

In the given point $(-3,-4)$ ,

the $x$ - coordinate is negative and the $y$ - coordinate is negative.

Therefore, it lies in the $III$ rd quadrant as shown in the graph.

$x$ co-ordinate is negative and $y$ co-ordinate is positive?

When

$x$ co-ordinate is negative and

$y$ co-ordinate is positive, point will lie in

$II$ quadrant.

Given below are some points, with their co-ordinates.
$$P(4, 3), Q(-3, 2), R(5, 1), S(0, -4)$$
What is the x-co-ordinate of point S ?

We know, any point in the

$xy$ cartesian plane, is denoted by

$(x-$ coordinate

$,y -$ coordinate

$)$
The point

$S$ is given as

$S(0,-4)$ .
Hence,

$x-$ coordinate of point

$S$ is

$0$ .

State on which axis or quadrant the following points belong:
$M(-3, -5), N(2, 0), S(0, -5), K(-2, 3), T(4, 0), E(7, 8), F(0, 1), O(0, 0)$ .

We know,

Point $(a,b)$ lies on the:

$x$ -axis if $b = 0$

$y$ -axis if $a = 0$ .

Also, the given point lies in the:

First quadrant, if $a > 0$ and $b > 0$ ,

Second quadrant, if $a < 0$ and $b > 0$ ,

Third quadrant, if $a < 0$ and $b < 0$ and

Fourth quadrant, if $a > 0$ and $b < 0$ .

Here,

Quadrant

$I$ :

$E(7,8)$ ,

Quadrant

$II$ :

$K(-2,3)$ ,

Quadrant

$III$ :

$M(-3,-5)$ ,

$Y$ -axis =

$F(0,1)$ and

$S(0,-5)$ ,

$X$ -axis =

$N(2,0)$ and

$T(4,0)$ and

Origin =

$(0,0)$ .

Plot the point $(5,-3)$ on a graph paper.

In the given point $(5,-3)$ , the x-coordinate is positive and the y-coordinate is negative.

Therefore, it lies in the $IV$ th quadrant as shown in the graph.

Write the co-ordinates of the following points in ordered pair:
Point $A$ : $y$ -co-ordinate is $1$ and $x$ -co-ordinate is $4$ .
Point $B$ : $x$ -co-ordinate is $3$ and $y$ -co-ordinate is $-5$ .
Point $C$ : $x$ -co-ordinate is $4$ and $y$ -co-ordinate is $0$ .
Point $D$ : $y$ -co-ordinate is $6$ and $x$ -co-ordinate is $0$ .

A point is denoted by

$(x- coordinate, y - coordinate)$ .

Hence, the points are:

$A(4, 1)$ ,

$B(3, -5)$ ,

$C(4, 0)$ ,

$D(0, 6)$ .

Plot the point $(5,0)$ on a graph paper.

In the given point $(5,0)$ ,

the x-coordinate is positive and the y-coordinate is zero.

Therefore, it lies on the positive $x$ -axis as shown in the graph.

Answer the question referring to the given graph:
The ordinate is $-4$ , if $D =(2,-4)$ .
If true enter $1$ , else $0$ .

We know, the abscissa is the

$x$ -coordinate, while the ordinate is the

$y$ -coordinate.

Also, in the

$xy$ -plane, any point is of the form

$(x,y)$ , where

$x,y$ can be any non-zero number.

Referring the graph, we can see that for the point,

$D = (2, -4)$ , the

$y$ -coordinate is

$-4$ and the point lies in the

$IV$ th quadrant.

Hence, the statement is true and

$1$ is the answer.

Plot the given points on a graph and join them together with a straight line:
$(0, -1), (2, 3), (-2, -5)$ and $(3, 5)$ .

The required graph is as shown.

Plot the given points on a graph and join them together with a straight line:
$(1, 2), (3, 3), (-1, 1)$ and $(-3, 0)$ .

The required graph is as shown.

Answer the question referring to the given graph:
The ordinate is $0$ if $B = (5, 0)$ .
If true enter $1$ , else $0$ .

We know, the abscissa is the

$x$ -coordinate, while the ordinate is the

$y$ -coordinate.

Also, in the

$xy$ -plane, any point is of the form

$(x,y)$ , where

$x,y$ can be any non-zero number.

Referring the graph, we can see that for the point,

$B = (5, 0)$ , the

$y$ -coordinate is

$0$ and the point lies on the

$x$ -axis.

Hence, the statement is true and

$1$ is the answer.

Write down the co-ordinates of the points $A$ to $J$ marked in the following diagram:

We know, a point is denoted by (

$x$ -coordinate,

$y$ -coordinate).

So, the points are:

$A = (2,1); B = (-2, 2); C = (-3, 3);$

$D = (-3, -3); E = (3, 0);$

$F = (0, 3); G = (-2, 0); H = (0, -1); I = (3, -2); J = (2, -3)$ .

The points where abscissa is $5$ are $B = (5, 0), H = (5, 5)$ and $G =(5, -3)$ .
If true, then enter $1$ and if false, then enter $0$ .

Since the abscissa or the $x$ -coordinate is $+5$ , we check the points which lies in the first or fourth quadrant with $x$ -coordinate $5$ and lie on the vertical line passing through $x= 5$ .

Observing the graph, points $B, H$ and $G$ lie on the vertical line passing through $x= 5$ and have $x$ -coordinate $= 5$ .

As the $y$ -coordinate of $B$ is $0$ , $\implies B =(5, 0)$ .

As the $y$ -coordinate of $H$ is $5$ , $\implies H= (5, 5)$ .

As the $y$ -coordinate of $G$ is $-3$ , $\implies G= (5, -3)$ .

Hence, the points are $B= (5, 0), H= (5, 5)$ and $G = (5, -3)$ .

Therefore, the given statement is true.

Hence, $1$ is the answer.

Referring to the given graph, the abscissa is $2$ if $A =(2, 2)$ .
If true enter $1$ , else enter $0.$

We know, the abscissa is the

$x$ -coordinate, while the ordinate is the

$y$ -coordinate.

Also, in the

$xy$ -plane, any point is of the form

$(x,y)$ , where

$x,y$ can be any non-zero number.

Referring the graph, we can see that for the point,

$A = (2, 2)$ , the

$x$ -coordinate is

$2$ .

Hence, the statement is true and

$1$ is the answer.

Answer the question referring to the given graph:
The ordinate is $3$ , if $C=(-4, 3)$ and $E = (6, 3)$ .
If true enter $1$ , else $0$ .

Since the ordinate or the $y$ -coordinate is $3$ , we look for the points lying on the horizontal line passing through $y=3$ or the points which have $y$ - coordinate $=3$ . Hence, the points lie in the $I$ or $II$ quadrant.

Observing the graph, both the points $C$ and $E$ lie on the horizontal line passing through $y=3$ and are the points which have $y$ - coordinate $=3$ .

As the $x$ -coordinate of $C$ is $-4$ , $C=(-4, 3)$ .
As the $x$ -coordinate of $E$ is $6$ , $E=(6, 3)$ .

Hence, the answer is $C=(-4, 3)$ and $E=(6, 3)$ .

That is, the statement is true.

Therefore, $1$ is correct.

Plot the point $(0,-4)$ on a graph paper.

In the given point $(0,-4)$ ,

the x-coordinate is zero and the y-coordinate is negative.

Therefore, it lies on the negative $y$ -axis as shown in the graph.

Plot the given points on a graph and join them together with a straight line:
$(2, 0), (4, 2), (-2, -4)$ and $(0, -2)$ .

The required graph is as shown.

$A$ $(- 2, 4), C (4, 10)$ and $D (- 2, 10)$ are the vertices of a square $ABCD$ . Use the graphical method to find the co-ordinates of the fourth vertex $B$ .
The co-ordinates of the mid-point of BC is $(m, 7)$ . The value of $m$ is

Plot the points

$A, C$ and

$D$ .

Join them using straight lines to complete the square. Hence

$B$

$=(4,4)$ .

Mid point of

$BC$

$=(4,7)$

Plot the following point on a graph paper: $(-3,0)$ .

The required point is

$B$ is as shown in the graph.
1980163_197483_ans_eeab522fdf3d47c38966a1174d8a2700.png

The abscissa is $2$ , the point is $(2,2)$ and $(2,-4)$ .
If true then enter $1$ and if false then enter $0$ .

Since the abscissa or the $x$ -coordinate is $2$ , we need to look for the points lying on the vertical line passing through $x=2$ or the points which have $x$ - coordinate $=2$ .

Observing the graph, both the points $A$ and $D$ are the points which have $x$ - coordinate $=2$ .

As the $y$ -coordinate of $A$ is $2$ , $A=(2,2)$ .
As the $y$ -coordinate of $D$ is $-4$ , $D=(2,-4)$ .

Hence, the answer is $A=(2,2)$ and $D=(2,-4)$ .

Therefore, the statement is true and $1$ is the answer.

Enter 1 if true else enter 0
Every point is located in one of the four quadrants.

1870452_185590_ans_0245083d18004e97b5543dbae2eac57e.jpeg

The ordinate is -The point is (2,-4).
If true then enter $1$ and if false then enter $0$ .

Since the ordinate or the $y$ -coordinate is $-4$ , we now look for the points lying on the horizontal line passing through $y=-4$ or the points which have $y$ - coordinate $= -4$ .

That is, the points will lie in the $III$ rd or $IV$ th quadrants.

Observing the graph, only the point $D$ has the $y$ - coordinate $= -4$ .

Also, the $x$ -coordinate of $D$ is $2$ , then $D=(2, -4)$

Hence, the answer is

$D(2, -4)$ .

Therefore, the given statement is true and

$1$ is the answer.

The ordinate is half of the abscissa, then the point $E=(6,3)$ .
If true, then enter $1$ and if false, then enter $0$ .

We know, the abscissa is the

$x$ -coordinate, while the ordinate is the

$y$ -coordinate.

Also, in the

$xy$ -plane, any point is of the form

$(x,y)$ , where

$x,y$ can be any non-zero number.

Referring the graph, we can see that for the point,

$E= (6, 3)$ , the

$y$ -coordinate

$3$ is half the

$x$ - coordinate

$6$

Hence, the statement is true and

$1$ is the answer.

The abscissa is equal to the ordinate, then $A = (2, 2), H = (5, 5)$ and $I = (4, 4)$ .
If true, then enter $1$ and if false, then enter $0$ .

We know, in cartesian plane, a point is represented in the form

$(x,y)$ .

Also, the abscissa is the

$x$ -coordinate and the ordinate is the

$y$ -coordinate.

When the abscissa is equal to the ordinate, then

$x=y=a$ .

Hence, the required points will be of the form

$(a,a)$ .

From the graph, the points of such form are

$A(2,2), H(5,5)$ and

$(4,4)$ .

Therefore, the given statement is true and hence,

$1$ is the answer.

See the figure and write the following:
(i) The Coordinates of $B$ .
(ii) The coordinates of $C$ .
(iii) The point identified by the coordinates $(-3, -5)$
(iv) The point identified by the coordinates $(2, -4)$ .
(v) The abscissa of the point $D$ .
(vi) The ordinate of the point $H$ .
(vii) The coordinates of the point $L$ .
(viii) The coordinates of the point $M$ .

(i) The coordinate of

$B$ is

$(-5, 2)$ .
(ii) The coordinate of

$C$ is

$(5, -5)$ .
(iii) The point identified by the coordinate

$(-3, -5)$ is

$E$ .
(iv) The point identified by the coordinate

$(2, -4)$ is

$G$ .
(v) Abscissa means

$x$ coordinate of the point

$D$ . So, the abscissa of the point

$D$ is

$6$ .
(vi) Ordinate means

$y$ coordinate of point

$H$ . So, ordinate of point

$H$ is

$-3$ .
(vii) The coordinates of the point

$L$ is

$(0, 5)$ .
(viii) The coordinates of the point

$M$ is

$(- 3, 0)$ .

Plot the following points on a graph sheet and verify if they lie on a line:
(a) $A(4,\,0),\,B(4,\,2),\,C(4,\,6),\,D(4,\,2.5)$
(b) $P(1,\,1),\,Q(2,\,2),\,R(3,\,3),\,S(4,\,4)$
(c) $K(2,\,3),\,L(5,\,3),\,M(5,\,5),\,N(2,\,5)$

$(a)$ The points

$A,B,C,D$ are plotted on the graph.

From the figure, we can observe they are in a straight line.

$(b)$ The points

$P,Q,R,S$ are plotted on the graph.

From the figure, we can observe they are in a straight line passing through the origin.

$(C)$ The points

$K,L,M,N$ are plotted on the graph.

From the figure, we can observe they are not in a straight line.

In which quadrant or on which axis do each of the points $(-2, 4), (3, -1), (-1, 0), (1, 2)$ and $(-3, -5)$ lie?
Verify your answer by locating them on the Cartessian plane.

Point

$(1,2)$ lies in the

$1^{st}$ quadrant.

Point

$(-2,4)$ lies in the

$2^{nd}$ quadrant.

Point

$(-3,-5)$ lies in the

$3^{rd}$ quadrant.

Point

$(3,-1)$ lies in the

$4^{th}$ quadrant.

Point

$(-1,0)$ lies on the negative side of

$x$ -axis.

(Street plan): A city has two main roads which cross each other at the center of the city. These two roads are along the North-South direction and East-West direction. All the other streets of the city-run parallel to these roads and are $200$ m apart. There are $5$ streets in each direction. Using $1$ cm $=200$ m, draw a model of the city on your notebook. Represent the roads/streets by single lines.
There are many cross-streets in your model. A particular cross-street is made by two streets, one running in the North-South direction and another in the East-West direction. Each cross street is referred to in the following manner: If the $2^{nd}$ street running in the North-South direction and $5^{th}$ in the East-West direction meet at some crossing, then we will call this cross-street $(2, 5)$ . Using this conversion, find: $(i)$ How many cross-streets can be referred to as $(4, 3)$
$(ii)$ How many cross-streets can be referred to as $(3, 4)$ .

$(i)$ Only one street can be referred to as

$(4, 3)$ as we see from the figure.

$(ii)$ Only one street can be referred to as

$(3, 4)$ as we see from the figure.

In the diagram,
Write the sum of coordinates of $U$

From the graph, we can see that the coordinate of

$U=(-2,4)$ .

Hence, the sum of coordinates=

$-2+4=2$ .

On the Cartesian plane above:
(a) Mark the point $A(-3, -2)$ ,
(b) Write the coordinates of the point $B$ .

The scale on

$x$ -axis is

$1:1$ and on

$y$ -axis is

$1:1$ .

(a) Point

$A(-3,-2)$ as

$-3$ on

$x$ -axis and

$-2$ on

$y$ -axis is marked as shown.

(b) The coordinates of the point

$B$ is

$(-4,3)$ .

On a certain Cartesian plane, the scale on the $x$ -axis is $1: 2$ , while the scale on the $y$ -axis is $1: 10$ .
Plot the following points:
$P(4, 80), Q(-6, 10), B(-4,-40), S(0, -20)$ .

The required points are as shown in the graph.

1130143_515261_ans_37a6c33f99884d2a82177045bda7cea9.png

Consider the number $3$ . Let us tabulate the multiples of $3$ , some positive and some negative.
$x$ $-3$ $-2$ $-1$ $0$ $1$ $2$ $3$
$3\times (-3)$ $3\times (-2)$ $3\times (-1)$ $3\times 0$ $3\times 1$ $3\times 2$ $3\times 3$
$y$ $-9$ $-6$ $-3$ $0$ $3$ $6$ $9$
$(x,y)$ $(-3,-9)$ $(-2,-6)$ $(-1,-3)$ $(0,0)$ $(1,3)$ $(2,6)$ $(3,9)$
Locate the points on a graph.

We will take a sheet of graph paper, and set up our own coordinate system

$X'OX\leftrightarrow Y'OY$ . Locate the points

$(x,y)$ tabulated in the last row.

In the above image, we can see that all these lie on a straight-line of the form

$y=3x$

Name the axis on which the following point lies.
(-5, -8)

For any point

$P(x,y)$ to lies on axes, either

$x=0$ or

$y=0$ .

Since both the coordinate of

$(-5,-8)$ are non-zero, hence it doesn't lies on axis.

But it lies on

$III$ quadrant.

Write the coordinates of the points marked in the graph.

We can see the given graph that point

$A$ is at a distance of

$3$ units from the

$y-axis$ and at a distance zero units from the

$x-axis$ .

Therefore, the

$x-coordinate$ of

$A$ is

$3$ and

$y-coordinate$ is

$0$ .

Hence, the coordinates of

$A$ are

$(3, 0)$ .

Similarly,

The coordinates of $B$ are $(2, 0).$
The coordinates of $C$ are $(-1, 0).$
The coordinates of $D$ are $(-2.5, 0)$ .
The coordinates of $E$ are $(-4, 0)$ .

So, as observed in figure, every point on the

$x-axis$ has

$0$ distance from the

$x-axis$ .

Therefore, the coordinate of a point lying on

$x-axis$ is always zero and the

$x-axis$ is denoted by the equation

$y = 0$ .

1034854_571121_ans_68eacd40511441aca6f0a2a849932769.png

Fix up your own coordinate system on a graph paper and locate the following points on the sheet:
$(i)$ $P(-3,5)$ ; $(ii)$ $Q(0,-8)$ ; $(iii)$ $R(4,0)$ ; $(iv)$ $S(-4,-9)$

1130150_557998_ans_38bdbb2907d74b2c8cf31a485a00f752.png

Plot at least six points in a graph sheet, each having the sum of its coordinates equal to 5.

1349445_571194_ans_67aba084b3a94cfeb3eb64bfb0490b57.PNG

Plot the following points in the graph paper and find out where they lie?
(i) A (2 , 3) (ii) B (-3 , 2) (iii) C (-5 ,-5) (iv) D (5 , -8) (v) E (6 , 0) (vi) F (-4 , 0) (vii) G (0 , 9) (viii) H (0 , -3) (ix) J (7 , 8) (x) O (0 , 0)

$A(2,3)$ lies in the $1^{st}$ quadrant $(+,+)$
$B(-3,2)$ lies in the $2^{nd}$ quadrant $(-,+)$
$C(-5,-5)$ lies in the $3^{rd}$ quadrant $(-,-)$
$D(5,-8)$ lies in the $4^{th}$ quadrant $(+,-)$
$E(6,0)$ lies on the x-axis
$F(-4,0)$ lies on the x'-axis
$G(0,9)$ lies on the y-axis
$H(0,-3)$ lies on the y'-axis
$J(7,8)$ lies in the $1^{st}$ quadrant $(+,+)$
$O(0,0)$ is the origin.

What can you say about the position of the points $(5, 4), (8, 4), (3, 4), (0, 4), (-4, 4), (-2, 4)$ ?

All points lie on a line parallel to X-axis at a distance of

$4$ units.

(2, 5), (4, 7)

2150775_571197_ans_4e45c7a739c54e85b7431439ed0b9f58.png

Plot the following points on a graph paper and find out where do they lie?
(i) A (7, 0) (ii) B (-5, 0) (iii) C (0 , 4) (iv) D (0, -3)

Draw the x and y axes. Mark the units along the x and y axes with a suitable scale.
(i) To plot the point A (7, 0)
Here, the x-coordinate of A is 7 which is positive and the y-coordinate of A is zero. Hence the point A (7, 0) lies on the x-axis. Start at the Origin. Move 7 units to the right along the x-axis and mark it.
(ii) To plot the point B (-5 , 0)
Here, the x-coordinate of B is 5 which is negative and the y-coordinate is zero. Hence the point B (-5 , 0) lies on the x-axis. Start at the Origin. Move 5 units to the left along the x-axis and mark it.
(iii) To lot the point C (0 ,4)
Here, the x-coordinate of C is zero and the y-coordinate of C is 4 which is positive. Hence the point C (0 , 4) lies on the y-axis. Start at the Origin. Move 4 units up along the y-axis and mark it.
(iv) To plot the point D (0 , -3)
Here the x-coordinate of D is zero and the y-coordinate of D is -3 which is negative. Hence the point D (0 , -3) lies on the y-axis. Start at the Origin. Move 3 units down along the y-axis and mark it.

State in which quadrant each of the following points lie without actually plotting the points.
(i) (8 , 15) (ii) (-15 , 2) (iii) (-20 , -10) (iv) (6 , -9) (v) (0 , 18) (vi) (-17 , 0) (vii) (9 , 0) (viii) (-100 , -200) (ix) (200 , 500) (x) (-50 , 7500).

$(8,15)$ lies in the $1^{st}$ quadrant $(+,+)$
$(-15,2)$ lies in the $2^{nd}$ quadrant $(-,+)$
$(-20,-10)$ lies in the $3^{rd}$ quadrant $(-,-)$
$(6,-9)$ lies in the $4^{th}$ quadrant $(+,-)$
$(0,18)$ lies on the y-axis
$(-17,0)$ lies on the x-axis
$(9,0)$ lies on the x-axis
$(-100,200)$ lies in the $3^{rd}$ quadrant $(-,-)$
$(200,500)$ lies in the $1^{st}$ quadrant $(+,+)$
$(-50,7500)$ lies in the $2^{nd}$ quadrant $(-,+)$

Plot the points $T(4, -2)$ and $V(-2, 4)$ on a cartesian plane. Whether these two coordinates locate the same point?

In this question we plotted two points

$T(4, -2)$ and

$V(-2, 4)$ . They are located on different points.

1034796_571184_ans_a791c91b975f40ceb926e425ad7b1c48.png

What can you say about the position of the points $(1, 2), (1, 3), (1, -4), (1, 0)$ and $(1, 8)$ .

All given points lie on a line parallel to

$Y$ -axis at a distance of

$1$ unit.

Plot the following point in the Cartesian plane
M (-2, 4)

Draw the

$x-axis$ and

$y-axis$ .

The given point is

$M(-2,4)$

We know that, the

$x-coordinate$ of a point is the perpendicular distance of the point from the

$y-axis$ and the

$y-coordinate$ is the perpendicular distance from the

$x-axis$ .

$\therefore \$ The point

$M$ will be at a distance of

$2$ units, towards left from the

$y-axis$ . Left because the

$x-coordinate$ is negative. Also, the point will be at

$4$ units distance from the

$x-axis$ upwards. Upwards because the

$y-coordinate$ is positive.

Hence, the point

$M$ lies in the second quadrant.

Finally, the position of the point

$M$ will be as shown in the above graph.

1111232_571178_ans_83017dfff9fb4dd09cdc1a9289b9ac1c.png

Draw the line joining the following points.
(i) A (2,3) and B (5, 7)

To draw the line joining the points A (2 , 3) and B(5 , 7):
First, plot the point (2 , 3) and denote it by A.
Next, plot the point (5 , 7) and denote it by B.
Then, join the points A and B. AB is the required line.

Plot the following points and draw a line through the points.
(i) (2 , 7) , (-2 ,-3) (ii) (5 , 4), (8 , -5) (iii) (-3 , 4), (-7 , -2) (iv) (-5 , 3), (5 , -1) (v) (2 , 0), (6 , 0) (vi) (0 , 7), (4 , -4)

1130174_618583_ans_3ced62b236094292b54faa7e2384177e.png

Draw a graph to show the area side of a square.

We know that the area of a square is the square of its side. (i.e)

$A = a^2$ .
(Here, A = Area, a = side). For different values of a, the values of A are given in the following table.

a (in cm)	1	2	3	4	5
$A = a^2 (in \,\,cm^2)$	1	4	9	16	25

Points: (1 , 1), (2 , 4), (3 , 9), (4 ,16), (5 , 25)
Plot the above points.
Join all the points. Observe the graph. Is it a linear graph? No. It is a curve.

Locate the points (i) $(3, 5)$ (ii) $(-2, -5)$ and $(-5, -2)$ in the rectangular coordinate system.

1066449_620439_ans_8ccfa2fe658c479abe93559b47746529.png

Find the coordinates of the points shown in the figure. Where each square is a unit square.

Consider the point A which is at a distance of 3 units from the origin along the positive direction of x-axis and 2 units distance from the origin along the positive direction of y-axis. Hence the coordinates of A are

$(3, 2)$ .
Similarly, B is

$(-3, 2)$ , C is

$(-2, -2)$ , D is

$(2, -1)$ , E is

$(5, -3)$ , F is

$(3, 4)$ and G is

$(-3, 1)$ .

Prove that the points (0, -5), (4, 3) and (-4, -3) lie on the circle centred at the origin with radius 5.

Distance from center to point on circle must be equal & equal to radius

$A=(0,-5) B(4,3) C(-4,-3) O(0,0)$

$AO=\sqrt{5^{2}}$

$BO=\sqrt{3^{2}+4^{2}}$

$CO=\sqrt{3^{2}+4^{2}}$

Hence

$CE(0,0)$ is center with radius 5.

Where does the point $(-2, 4)$ lie in the coordinate plane?

Point

$(-2,4)$ have negative abscissa and positive ordinate i.e, is in the

${ 2 }^{ nd }$ quadrant

Plot the point $A(0,3), B(5,3), C(4,0)$ and $D(-1,6)$ on the graph paper. The figure $ABCD$ and find whether the point $(2,2)$ his inside the figure or not

The point

$(2, 2)$ lies inside the figure.
1011166_1061343_ans_43b639d1839248048f58a6547f3aae0d.png

In the seating arrangement of desks in a classroom three students Rohini, Sandhya and Bina are seated at $A(3,1),B(6,4)$ and $C(8,6)$ . Do you think they are seated in a line?

Rohini -

$A(3,1)$

Sandhya -

$B(6,4)$

Bina -

$C(8,6)$

If Three students are sitting in line then they should satisfied atleast one of the following Condition

$AC=AB+BC\ \overset { o }{ A } \ \overset { o }{ B } \ \overset { o }{ C }$

$BC=AB+AC\ \overset { o }{ B } \ \overset { o }{ A } \ \overset { o }{ C }$

$AB=AC+BC\ \overset { o }{ A } \ \overset { o }{ C } \ \overset { o }{ B }$

Now, find the length

$AB=\sqrt {(6-3)^2 +(4-1)^2}$

$AB=\sqrt {9+9}$

$AB=3\sqrt {2}$

$BC=\sqrt {(8-6)^2 +(6-4)^2}$

$BC=\sqrt {4+4}=2\sqrt {2}$

$AC=\sqrt {(8-3)^2 +(6-1)^2}$

$AC=\sqrt {25+25}=5\sqrt {2}$

Then This is satisfied

$AB+BC=CA$

Hence the Three places

$A, B, C$ is in line

So, that three student sitting in a line.

Draw x and y axes and mark the points $A(-1, 2), B(6, 3).$

State in which quadrant or on which axis do the following points lie.
i) A(-3, 2) , ii) B(-5, -2), iii) K(3.5, 1.5) , iv) D(2, 10), v) E(37, 35), vi) F(15, -18) , vii) G(3, -7), viii) H(0, -5),

1045268_1060116_ans_bed13b1babbe4832a98fe5d174f39634.png

In which quadrant would the following point be found:
$(1, 1)$

Given point is

$\left( { 1,1 } \right)$ .

As both the

$x-coordinate$ as well as the

$y-coordinate$ are positive, the point will lie in the first quadrant.

Hence,

$(1,1)$ lies in the first quadrant.

1196707_1316428_ans_8326cd51e2ee4fa38d5d28bde5cbd991.png

The point (-3, -2) lies in which quadrant?

$x < 0$ &

$y < 0$

$\Rightarrow III^{rd}$ Quadrant.

1167381_1267380_ans_d036bea254da483b8dff81e539e2242a.jpg

Plot the points $A(2,0),$ $B(5,0),$ $C(5,3)$ and $D(2,3)$ . Name the figure obtained by joining the points $ABCD$ .

1323431_1079790_ans_0db78339bc8146f5b49f813d2800d4b8.PNG

In which quadrant will the point $(1, 2)$ be lying?

Given the point is

$\left( { 1,2 } \right)$

As the

$x$ co-ordinate is positive and

$y$ co-ordinate is positive, so the point lies in the first quadrant.

1196719_1316429_ans_a207b80a6829442887f3447bc4eda3a7.png

Write the quadrants or axis to which the following points belongs:
$A(2,-3), B(4,1), C \left(-5, \dfrac{-3}{2}\right), D (3,0), E (-3, 4), F (0,-5), G (-1, 0), H(3,3).$

1339248_1203000_ans_ce291ff6a9764e0ab606908b2b503e41.jpg

From the figure, find the coordinates of $A,B,C,D,E$ and $F$ . Which of the points are mirror image in (i)x-axis ,(ii)y-axis

coordinates of point is given as:

A=(2,2)

B=(1,4)

C=(5,5)

D=(0,4)

E=(2,-2)

F=(-5,-5)

(i) point A and E are mirror image in x-axis

(ii) There is no mirror image in y-axis

Write the quadrant or axis to which the following points belong : A(2, -3) ; B(4, 1) ; C(-5, -3/2) ; D(3, 0), E(-3, 4), F(0, -5), G(-1, 0) , H(3, 3).

1326515_1063384_ans_c080879128224c18bec8b2d3627f13e5.jpg

In which quadrant or on which axis each of the following points lies. Write abscissa and ordinate each of the following:
(i) (3, -4)
(ii) (-3, 5)
(iii) (-10, 0)
(iv) (-2, -7)

(i)

$3 , -4$

absicca

$= 3$ ordinate

$= -4$

since absicca is possitive and ordinate negative , it lies in

$4th$ quadrant

(ii)

$-3 , 5$

absicca

$= 3$ ordinate

$= 5$

since absicca is negative and ordinate is positive, it lies in

$2nd$ quadrant

(iii)

$-10. 0$

absicca

$= -10$ ordinate

$= 0$

since the ordinate is

$0$ , this point lies on the

$x-axis$

(iv)

$-2 , -7$

absicca

$= -2$ ordinate

$= -7$

since absicca and ordinate , both are negative, this point lies in

$4th$ quadrant

If $x<0$ and $y>0$ , then $(-x,y)$ lies in which quadrant ?

$x<0 \implies -x>0$

Therefore, the point

$(-x,y)$ lies in the frist quadrant.

Find the intercepts cut off by the line $x+y-1=0$ on the axes.

$x-$ intercept:Put

$\,y=0$

$\therefore\,x-1=0$

$\Rightarrow \,x=1$ is the

$x-$ intercept

$y-$ intercept:Put

$\,x=0$

$\therefore\,y-1=0$

$\Rightarrow \,y=1$ is the

$y-$ intercept.

In the figure, $OABC$ is a rectangle and its breadth is $3$ . Write the co-ordinates of the vertices $B$ and $C$ .

Given that

$OABC$ is a rectangle.

Length

$=6\ \text{units}$
Breadth

$= 3\ \text{units}$
Co-ordinates of

$A$ are

$(6, 0)$ .

From the figure,

$AB = 3\ \text{units}$ (breadth)
Hence, coordinates of

$B$ are

$(6,3)$ .

$OC=3\ \text{units}$

Hence, the co-ordinates of

$C$ are

$(0, 3)$ .

1223381_1579634_ans_194c7b40cefe470ea98b1e5e27fc8092.PNG

In which quadrant does the point lie if the ordinate is $2$ units and the abscissa is $-3$ units.

Ordinate

$=$ y coordinate

$= 2$

Abscissa

$=$ x coordinate

$=-3$

$\therefore$ It lies in the second quadrant, where x is negative but y is positive.

In what ratio is the line segment joining $\left(1,3\right)$ and $\left(7,9\right)$ divided by the line $x+y=3?$

The given line is

$x+y=3$ ..........

$(1)$

Let the line

$(1)$ divide the line segment joining the point

$\left(1,3\right)$ and

$\left(7,9\right)$ at the point

$P$ in the ratio

$k:1$ then the co-ordinates of point

$P$ are

$\left(\dfrac{7k+1}{k+1},\dfrac{9k+3}{k+1}\right)$

Section formula,

$\left(x,y\right)=\left(\dfrac{m{x}_{2}+n{x}_{1}}{m+n},\dfrac{m{y}_{2}+n{y}_{1}}{m+n}\right)$

Since

$P$ lies on

$(1)$ , we get

$\dfrac{7k+1}{k+1}+\dfrac{9k+3}{k+1}=3$

$\Rightarrow\,7k+1+9k+3=3k+3$

$\Rightarrow\,16k+4=3k+3$

$\Rightarrow\,16k-3k=3-4$

$\Rightarrow\,13k=-1$

$\Rightarrow\,k=\dfrac{-1}{13}$

Hence, the required ratio is

$\dfrac{-1}{13}:1$ or

$1:13$ externally.

For the following points, write the quadrant in which it lies. $\displaystyle (3, -8)$

In the given point

$\displaystyle (3, -8)$

The x-coordinate

$3$ is positive and the y-coordinate

$-8$ is negative.

Therefore,

$\displaystyle (3, -8)$ lies in the

$\displaystyle IV$ quadrant.

What are the points on the $y-$ axis whose distance from the line $\dfrac{x}{3}+\dfrac{y}{4}=1$ is $8$ units.

The given line is

$\dfrac{x}{3}+\dfrac{y}{4}=1$

$4x+3y-12=0$ ........

$(1)$

Let

$\left(0,k\right)$ be a point on the

$y-$ axis whose perpendicular distance from the line

$(1)$ is

$8$ units, then

$\dfrac{\left|4\times 0+3\times k-12\right|}{\sqrt{{4}^{2}+{3}^{2}}}=8$

$\Rightarrow\,\dfrac{\left|3k-12\right|}{\sqrt{16+9}}=8$

$\Rightarrow\,3k-12=\pm\,8$

$\Rightarrow \,3k=12\pm\,40$

$\Rightarrow\,3k=52,\,-28$

$\therefore\,k=\dfrac{52}{3},\,\dfrac{-28}{3}$

$\therefore\,k=14,\,\dfrac{-28}{3}$

Hence the required points are

$\left(0,14\right)$ and

$\left(0,\dfrac{-28}{3}\right)$

In which quadrant do the point (4,-2) lie ?

In the point (4,-2) abscissa is positive and ordinate is negative. So, it lies in fourth quadrant.

State in which quadrant or on which quadrant do the following point lie.
$A(-3,2)$

Given the point is

$A(-3,2)$ , of which

$x$ co-ordinate is negative and

$y$ co-ordinate is positive. So the point lies on second quadrant.

On a graph paper, plot the each of the following points:
(i) A $(4,3)$
(ii) B $(-2,5)$
(iii) C $(0,4)$
(iv) D $(7,0)$
(v) E $(-3,-5)$
(vi) F $(5,-3)$
(vii) G $(-5,-5)$
(viii) H $(0,0)$

Points

$A,B,C,D,E,F,G,H$ are plotted in figure.
1618001_1775158_ans_8a5a24c3ba8c486d9599c61277263bf1.png

From the given graph, choose the letter that indicates the location of the point $(2, 6)$ $

$(2,6)$ is the point lying at a distance of

$2$ units from the

$y$ axis is and at a distance is

$6$ unit from the

$x$ axis.

According to the given graph,

$C$ is the point that represents the position of the point

$(2, 6)$ .

The

$x$ coordinate of point

$C$ is

$2$ and

$y$ coordinate is

$6.$

From the given graph, choose the letters that indicate the location of the points given below.
$(5, 1)$

$(5,1)$ is the point lying whose distance from the

$y$ axis is

$5$ units and from

$x$ axis is

$1$ unit.

According to the given graph.

$H$ is the point that represents the position of the point

$(5, 1)$ . In the given graph, the x-coordinate is

$5$ and y-coordinate is

$1$ .

A point in which the x - coordinate is zero and y- coordinate in non-zero will lie on the ________.

A point in which the x - coordinate is zero and y- coordinate in nonzero will lie on the y-axis.

From the given graph, choose the letters that indicate the location of the points given below.
$(2, 0)$

$(2,0)$ is the point lying on

$x$ axis at a distance

$2$ units from the origin.

According to the given graph,

$F$ is the only point that represents the position of the point

$(2, 0)$ , whose x-coordinate is

$2$ and y-coordinate is

$0$ .

From the given graph, choose the letters that indicate the location of the points given below.
$(0, 4)$

$(0,4)$ is the point lying on

$y$ axis at a distance

$4$ units from origin.

According to the given graph.

$A$ is the only point that represents the position of the point

$(0,4)$ , whose x-coordinate is

$0$ and y-coordinate is

$4$ .

Plot the given points on a graph sheet and check if the points lie on a straight line. If not, name the shape they from when joined in the given order.
$(1, 1), (1, 2), (2, 1), (2, 2)$

The given points are plotted in the graph sheet as shown.

After plotting the given points, we observe that they do not lie on a straight line, instead, they make a square.

1689889_1794287_ans_6f878a7c68014a82a4848e6dbac52810.png

Plot the given points on a graph sheet and check if the points lie on a straight line. If not, name the shape they form when joined in the given order.
$(4, 2), (2, 4), (3, 3), (5, 4).$

The given points are plotted in the graph sheet as shown.

After plotting the given points, we observe that they do not lie on a straight line, instead, they make a triangle.

1689897_1794288_ans_008a3e13440342449b6e35d23087f367.png

Plot the given points on a graph sheet.
a) $(5, 4)$
b) $(3, 1)$
c) $(3, 1)$
d) $(0, 4)$
e) $(4, 5)$

1688903_1794240_ans_8323d29b12a44e8d9ad7792037ad68cd.png

If y-coordinate is 3 times x-coordinate, form a table for it and draw a graph.

$x$ $1$ $2$ $3$ $4$
$y$ $3$ $6$ $9$ $12$

As per question, the graph is plotted as shown.
1689901_1794303_ans_7c7006406db94ed08525cb65fcbc4495.png

Find the coordinates of all the letters in the graph given above.

From the graph,

The coordinate of point

$A = (0, 7.5)$

The coordinate of point

$B = (4, 5)$

The coordinate of point

$C = (7.5, 2.5)$

The coordinate of point

$D = (11, 0)$

The coordinate of point

$E = (14.5, 6.5)$

The coordinate of point

$F = (18, 10)$

Points $A \left(5,3\right), B \left(-2,3\right)$ and $D \left(5,-4\right)$ are three vertices of a square ABCD. plot these points on a graph paper and hence find the coordinates of the vertex C.

The graph obtained by plotting the points A,B and C and D is given below. Take a point C on the graph such that ABCD is square i.e ..., all sides AB, BC, CD and AD are equal. So, abscissa of C should be equal to abscissa of B i.e ...,

−2.

1904239_1794544_ans_39aafea573db458ca20da540d85d82e7.PNG

Find the coordinates of the vertices of the given figures.

In figure l,

The coordinates of its vertices :

$(1, 1), (2, 3), (4, 2 )$ and

$(3, 0)$ .

In figure ll,

The coordinates of its vertices :

$(0, 5), (2, 4)$ and

$(1, 2)$ .

In figure lll,

The coordinates of its vertices :

$(1, 5), (2, 6), (3, 6), (4, 5), (2,4)$ and

$(2,5)$ .

In figure lV,

The coordinates of its vertices :

$(1, 2), (3, 0), (4, 2)$ and

$(2,3)$

In which quadrant or on which axis each of the following points lie?
$(-3, 5), (4, -1) (2, 0), (2, 2), (-3, -6)$

In first quadrant, both

$x$ and

$y$ coordinate are positive.
In second quadrant,

$x-coordinate$ is negative and y-coordinate is positive.
In third quadrant,

$x-coordinate$ is negative and y-coordinate is negative.
In fourth quadrant,

$x-coordinate$ is positive and y-coordinate is negative.

$(-3,5)$ lies in second quadrant.

$(4,-1)$ lies in fourth quadrant.

$(2,0)$ lies on x-axis. Here y-coordinate is zero.

$(2,2)$ lies in first quadrant.

$(-3,-6)$ lies in third quadrant.

Plot the following points on the same graph paper :
$A (3, 4), B (-3, 1), C (1, -2), D (-2, -3), E (0, 5), F (5, 0), G (0, -3), H (-3, 0).$

Given points are

$A (3, 4), B (-3, 1), C (1, -2), D (-2, -3), E (0, 5), F (5, 0), G (0, -3), H (-3, 0).$
The points are plotted in the graph below.
1721641_1811846_ans_35f9839e83e349ce9a7f3f7d33521cc2.PNG

Taking $0.5$ cm as $1$ unit, plot the following points on the graph paper:
$A \left(1,3\right), B \left(-3,-1\right),C \left(1,-4\right), D \left(-2,3\right), E \left(0,-8\right), F \left(1,0\right)$

Here, in point

$A \left(1,3\right)$ both

$x \, and \, y$ - coordinates are positive, so its lies in

$I$ quadrant. In point

$B \left(-3,-1\right)$ , both x and y - coordinates are negative, so it lies in

$III$ quadrant. In point

$C \left(1,-4\right)$ x- coordinate is negative and y- coordinative is positive, so it lies in

$II$ quadrant. In point

$E \left(0,8\right)$ x - coordinate is zero, so it lies on y - axis and in point

$F \left(1,0\right)$ y - coordinate is zero, so it lies on x -axis. On plotting the given points, we can get the graph.
1904598_1794527_ans_5101846f775b401db1fefa737ce04dea.PNG

1904598_1794527_ans_5101846f775b401db1fefa737ce04dea.PNG

Write the coordinates of each of the points P,Q,R,S,T and O from the Fig, $3.5$

The coordinates of the points P,Q,R,S,T and O are

$P \left(1,1\right), Q \left(-3,0\right), R \left(-2,-3\right), S \left(2,1\right), T \left(4, -2\right)$ and

$O \left(0,0\right)$

Which of the following points lie on
(i) $x-axis?$ (ii) $y-axis?$
$A (0, 2), B (5, 6), C (23, 0), D (0, 23), E (0, -4), F (-6, 0), G (3,0)$

Given points are

$A (0, 2), B (5, 6), C (23, 0), D (0, 23), E (0, -4), F (-6, 0), G (3,0)$

(i) If

$y-coordinate$ of a point is zero, then the point lies on

$X-axis.$
So

$C(23,0), F(-6,0)$ and

$G(3,0)$ lies on

$X-axis.$

(ii) If

$x-coordinate$ of a point is zero, then the point lies on

$Y-axis.$
So

$A(0,2), D(0,23)$ and

$E(0,-4)$ lies on

$Y-axis$ .

The points on the graph below represent the height and weight of the donkey, dog, crocodile, and ostrich shown in the drawing.
Which point repesents each animal? Expalin.

We have four animals Donkey, Dog, Crocodile and Ostrich.

Order of Height : Ostrich > Donkey > Dog > Crocodile

Order of Weight : Crocodile > Donkey > Ostrich > Dog

Now we can observe following things from the graph :

1. Point D represents Ostrich because it is tallest among donkey, dog, crocodile.

2. Point B represents Donkey as after Ostrich it is second tallest among the group.

3. Point A is for Crocodile as it smallest among all the given animals.

4. Point C represents Dog as it is smallest among all.

Plot the following points on the same graph paper :
$\displaystyle A(2, \frac{5}{2}), B(\frac{-5}{2}, 3), C(\frac{1}{2}, \frac{-3}{2})$ and $D(\dfrac{-5}{2}, \dfrac{-1}{2}).$

Given points are

$\displaystyle A(2, \frac{5}{2}), B(\frac{-5}{2}, 3), C(\frac{1}{2}, \frac{-3}{2})$ and

$D(\dfrac{-5}{2}, \dfrac{-1}{2}).$
The points are plotted in the graph below.
1721655_1811850_ans_bd0d3ada8f5545688fa26404fe8e657a.PNG

Where does the point having y - coordinate -5 lie ?

The point having -5 lies on the y-axis on the negative side because here x-axis is o and when x-axis is o then points lies on the y-axis and when y-axis is o then point lies on the x-axis.
We can show it on graph with points

(0,−5).

1794021_1815592_ans_2250e1ab119a422db2d8dc95d5feba76.png

Use the table given alongside to draw the graph of a straight line. Find, graphically the values of $a$ and $b.$
$x$ $1$ $2$ $3$ $a$
$y$ $-2$ $b$ $4$ $-5$

First, we will plot the points

$(1,-2)$ and

$(3,4)$ on the graph and join and extend them to get a line.

Now, try to locate the point on the line whose abscissa is equal to

$2.$

Now, try to locate the point on the line whose ordinate is equal to

$-5.$

After locating, the unknown points on the graph we get that value of

$a$ is

$0$ and

$b$ is

$1.$

1724953_1812087_ans_58003b0977514ff6aef27613621184c8.PNG

In which quadrant do the point $(0, -5)$ lie?

Given point is $$

(0,−5)$$(0,−5). This point lies on the y-axis because it's

$x$ coordinate is

$0$ .

Therefore, it lies on the y-axis between Quadrant III and Quadrant IV.

1793964_1815584_ans_d9267b0a083544caa8fe6a960a0ffbba.png

In which quadrants do the following points like:
$(-8, 6)$

Given coordinate

(−8,6)(−8,6) lies in Quadrant II because as shown in the figure that those points which have a sign like this

(−,+)(−,+) lies in II quadrants. So

(−8,6)(−8,6) lies in III Quadrant. Here also x-axis point is "-" and y-axis point is "+" so

(−8,6)(−8,6) lies in Quadrant II.
1793961_1815581_ans_a60a1957627b40b5942edfcd6ac19d90.png

In which quadran do the following point lie:
$(-4, -6)$

Given coordinate

$(-4, -6)$ lies in Quadrant III because as shown in figure that those points which have a sign pattern like this

$(-, -)$ or can say whose both

$x-coordinate$ and

$y-coordinate$ is negative lies in quadrant lll . So

$(-4, -6)$ lies in Quadrant lll.

1793959_1815578_ans_9b81cadede3e4900bb3c93270aedc0ac.png

In which quadrants do the following points like:
$\left ( \dfrac{3}{2}, 5 \right)$

Giveorn coordinate

(32,5)(32,5) lies, in Quadrant I because as shown in figure that those codinate who have

(+,+)(+,+) sign lies in IV quadrants or can say whose x-axis is "+" and y-axis is also "+" lies in I Quadrant.
1793962_1815582_ans_cc5c54513b47476383ff7587c0b41aab.png

1793962_1815582_ans_cc5c54513b47476383ff7587c0b41aab.png

In which quadrants do the following points like:
$(3, 0)$

Given coordinate is

(3,0)(3,0). This point lies on the x-axis because its y-axis is on origin. Therefore, it lies on the x-axis between the Quadrant I and Quadrant IV.
1793963_1815583_ans_249d9f539c7a41cfad3a25fd90a368f4.png

1793963_1815583_ans_249d9f539c7a41cfad3a25fd90a368f4.png

Draw the triangle whose vertices are $(2, 3), (-4, 2)$ and $(3, -1).$

In which quadrants do the following points lie:
$(10, -3)$

Given coordinate

(10,−3)(10,−3) lies in Quadrant IV because as shown in the figure that those coordinate who have

(+,−)(+,−) sign lies in IV quadrants, or can say whose x-axis is "+" and y-axis is "-" lies in IV Quadrant.
1793957_1815575_ans_5a626434c6504422aec2507dee1c6811.png

State on which axis do the following point lie.
M $( 12 , 0 )$

The

$y$ coordinate of M

$(12 , 0 )$ is zero. Therefore, point M

$( 12, 0 )$ is on the

$X$ - axis .

State in which quadrant or on which axis do the following points lie:
B $( - 5 , -2 )$

Given point is

$B(-5,-2)$ .

We can see that both the

$x-coordinate$ and

$y-coordinate$ are negative.

Therefore , point

$B( -5 , - 2 )$ will lie in the third quadrant.

State in which quadrant or on which axis do the following points lie
F $( 15 , -18 )$

The

$x$ coordinate of F

$( 15 , -18 )$ is positive and the

$y$ coordinate is negative. Therefore , point F

$( 15 , -18 )$ is in the fourth quadrant .

State in which quadrant or on which axis do the following point lie:
A $( -3 , 2 )$

Given point is

$A(-3,2)$ .

We can see that, the

$x-coordinate$ of

$A$ is negative and its

$y-coordinate$ is positive.

We know that, in the second quadrant, the

$x-coordinate$ is negative and

$y-coordinate$ is positive.

Hence, the point

$A( -3 , 2 )$ lies is in the second quadrant.

State in which quadrant or on which axis do the following points lie
E $( 37 , 35 )$

The x co - ordinate of E

$( 37 , 35)$ is positive and its y coordinate is positive . Therefore , point E

$( 37 , 35 )$ is in the first quadrant .

State in which quadrant or on which axis do the following points lie
C $( 3.5 , 1.5 )$

The x co - ordinate of K

$( 3.5 , 1.5 )$ is positive and its y coordinate is positive . Therefore , point K

$( 3.5 , 1.5 )$ is in the first quadrant .

State in which quadrant or on which axis do the following point lie.
D $( 2 , 10)$

The

$x$ coordinate of D

$( 2, 10)$ is positive and its

$y$ coordinate is positive. Therefore, point D

$( 2, 10 )$ is in the first quadrant.

State in which quadrant or on which axis do the following points lie
N $( 0 , 9)$

The

$x$ co - ordinate of

$N$

$(0,9)$ is on the

$Y$ - axis.Therefore , point

$N$

$( 0 , 9 )$ is on the

$Y$ - axis .

State in which quadrant or on which axis do the following points lie
G $( 3 , -7 )$

The

$x ,$ co - ordinate of G

$( 3 , -7 )$ is positive its

$y$ coordinate is negative . Therefore , point G

$( 3 , - 7 )$ is in the fourth quadrant .

State in which quadrant or on which axis does the following point lie :
A $( 0 , -5 )$

The given point is

$A(0,-5)$

The

$x$ coordinate of

$A( 0 , - 5 )$ is zero .

Therefore , point

$A( 0 , - 5 )$ lies on the

$Y - axis$ .

State in which quadrant or on which axis do the $P ( 0 , 2.5 )$ point lie on.

The

$x$ co-ordinate of point

$P ( 0 , 2.5 )$ is zero. Therefore, point

$P ( 0, 2.5 )$ lies on

$y$ - axis.

State in which quadrant or on which axis do the following points lie
E $( -7 , -3 )$

The x co - ordinate of Q

$( - 7 , - 3 )$ is negative and its y coordinate is negative . Therefore , point Q

$( -7 , - 3 )$ is in the third quadrant.

Draw the co - ordinate system on a plane and plot the following points .
L $( - 2 , 4 ), M ( 5 , 6) , N (-3 , -4) , P (2, -3), Q (6 , -5), S ( 7, 0 ), T ( 0 , -5)$

The given points are

$L(-2, 4), M(5,6), N(-3,-4), P(2,-3), Q(6,-5), S(7, 0)$ and

$T(0, -5)$ . These point can be plotted on the co-ordinate system as follows:

1807259_1855735_ans_1680e1da0e114eaa94881870ae66b661.png

In which quadrant are the following points
Whose both co - ordinate are negative

The x co- ordinate and y co - ordinate of a point negative in the third quadrant .

In which quadrant are the following points ?
Whose x co - ordinate is negative and the y co - ordinate is positive

The x co - ordinate of a point is negative and y co - ordinate of a point is positive in the second quadrant .

In which quadrant are the following points ?
Whose x co - ordinate is positive, and the y co - ordinate is negative .

The x co - ordinate is positive, and the y co - ordinate is negative in the fourth quadrant .

On a graph paper plot the points A $( 3, 0 ) , B (3,3), C (0 , 3)$ . Join A , B and B, C .What is the figure formed ?

The given points are

$A(3, 0), B(3,3)$ and

$C(0, 3)$ . These points can be plotted on the co-ordinate plane as follows:
1807266_1855737_ans_2624a7d8db6a434ea0427318436f7056.png

Some points are shown in the given figure , With the help of it answer the following questions :
Write the co - ordinates of the points Q and R .

The

$x$ co - ordinate of a point is its distance from the

$Y -$ axis and

$y$ co - ordinate of a point is its distance from the

$X -$ axis .
The co - ordinates of point

$Q$ are

$(-2 , 2 )$ and The co - ordinates of point

$R$ are

$( 4 , -1 )$ .
1819542_1855774_ans_b48d0a890c454696838cee94552482aa.png

Without plotting the point on a graph , state in which quadrant or on which axis do the following point lie.
$( - 23 , 4 )$

The

$x$ co - ordinate of the point

$( -23, 4 )$ is negative and its

$y$ co - ordinate is positive .

Therefore , the point

$( -23 , 4 )$ lies in the second quadrant .

Without plotting the point on a graph , state in which quadrant or on which axis do the following point lie.
$( -7 , -12 )$

The

$x$ co - ordinate of the point

$( -7, -12 )$ is negative and its

$y$ co - ordinate is negative .

Therefore , the point

$( -7 , -12 )$ lie in the third quadrant .

Without plotting the point on a graph , state in which quadrant or on which axis do the following point lie.
$( 0 . -3 )$

The x co - ordinate of the point

$( 0 , -3 )$ is zero . Therefore , the point

$( 0 , -3)$ lie on the Y - axis .

Some points are shown in the given figure , With the help of it answer the following questions :
Write the points lies in the third quadrant ?

The point whose

$x$ co - ordinate is negative and

$y$ co - ordinate is negative lies in the third quadrant .
Thus , the point

$S ( -3 , - 2 )$ lies in the third quadrant .
1819677_1855776_ans_fca8fe1df4654b759016f073a08f07ee.png

Some points are shown in the given figure , With the help of it answer the following questions :
Write the co - ordinates of the points T and M

The

$x$ co - ordinate of every point on the

$Y -$ axis is

$0$ and the

$y$ co -ordinate of every point on the

$X -$ axis is

$0$ .
The co - ordinates of point

$T$ are

$( 0 , -1 )$ and the co - ordinates of point

$M$ are

$( 3, 0 )$ .
1819659_1855775_ans_c844fea2549d4adb9b222e7fc3bba814.png

Some points are shown in the given figure , With the help of it answer the following questions :
Write are the points whose x and y co - ordinates are equal ?

The co - ordinates of point

$O$ are

$(0 , 0 )$
Thus ,

$O$ is the point whose

$x$ and

$y$ co -ordinates are equal
1819685_1855777_ans_7036d0626aa249b0b15ed69ed46fdb92.png

Without plotting the point on a graph , state in which quadrant or on which axis do the following point lie.
$( 5 , -3 )$

The x co - ordinate of the point

$( 5 , -3 )$ is positive and its y co - ordinate is negative . Therefore , the point

$( 5 , -3 )$ lie in the fourth quadrant .

Without plotting the point on a graph, state in which quadrant or on which axis do the following point lie.
$( - 9 , 5 )$

The

$x$ coordinate of the point

(−9,5)(−9,5) is negative and

$y$ coordinate is positive.

Therefore, It lies in the second quadrant.

Without plotting the point on a graph , state in which quadrant or on which axis do the following point lie.
$( -6 , 0 )$

The

$y$ co-ordinate of the point

$( -6 ,0 )$ is zero .

Therefore , the point

$( -6 , 0 )$ lie on the

$x$ - axis. Any point on

$x$ axis is in the form of

$(x,0)$ .

In the graph alongside, line LM is parallel to the Y-axis
Write the coordinates of the points P, Q, and R.

The coordinates of a point are it's perpendicular distances from the

$x$ and

$y$ axes.

$\therefore$ the coordinates of the points

$P, ~Q$ and

$R$ are

$( 3,2 ),(3,-1)$ and

$( 3, 0 )$ , respectively .

1819813_1855803_ans_a6a613f859f5400ab2468b3cd27f95cd.png

Draw a quadrilateral, if its vertices are following:
(1,1), (2,4), (8,4) and (10,1)
Also mention the type of the obtained quadrilateral.

First draw two perpendicular axis XOX' and YOY', let the vertices of quadrilateral are

$P(1,1), Q(2,4), R(8,4)$ and

$S(10,1)$
Draw these points of the coordinate axis as shown:

It is clear from the figure, sides PS and QR are parallel and sides PQ and RS are unequal.
Hence given quadrilateral is trapezium.
1857478_1876338_ans_b2d47b2d5ded4da5b5ce0930c44ea484.png

1857478_1876338_ans_b2d47b2d5ded4da5b5ce0930c44ea484.png

See Fig.14, and write the following:

(i) The coordinates of

$B : (-5, +2)$
(ii) The coordinates of

$C. : (+5, -5)$
(iii) The point identified by the coordinated

$(-3, -5) : E$ .
(iv) The point identified by the coordinated

$(2, -4) : G$ .
(v) The abscissa of the point

$D : 6$
(vi) The ordinate of the point

$H : -3$ .
(vii) The coordinates of the point

$L : (0, +5)$
(viii) The coordinates of the point

$M : (-3, 0)$ .

In which quadrant or on which axis do each of the points $(-2, 4), (3, -1), (-1, 0), (1, 2)$ and $(-3, 5)$ lie? Verify your answer by locating them on the Cartesian plane.

$A (-2, 4)$ II Quadrant

$B (3, -1)$ IV Quadrant

$C(-1, 0)$ Negative x-axis

$D (1, 2)$ I Quadrant

$E (-3, -5)$ III Quadrant
1830098_1869680_ans_4e953f01a9a04c7f95e2a2dc762d175d.png

Plot the points of following coordinates;
(1,2),(-1,3),(-2,-4),(3,-2),(2,0),(0,3)

In the question for plotting points draw two axis XOX' and YOY' and mark the points

$P(1,2),Q(-1,3),R(-2,-4),S(3,-2),T(2,0),L(0,3)$
1857429_1876309_ans_a7990034742845e7ba5cbab4e9a94d6b.png

Write the answer of each of the following questions :
(i) What is the name of horizontal and the vertical lines drawn to determine the position of any point in the Cartesian plane?

(i) In a Cartesian plane, to determine the position of any point, horizontal line is called x-axis. Vertical line is y-
The y-coordinate is also called the ordinate.
Horizontal line

$\rightarrow$ xOX'
Vertical line

$\rightarrow$ yOY'

Plot the following points on the one and the same co - ordinate system .
A $( 1, 3 ) , B ( -3 , -1 ) , C ( 1 , -4 ) , D ( -2 , 3 ) , E ( 0 , -8 ), F ( 1, 0 )$

The given points are

$A( 1, 3 ) , B ( -3 , -1 ) , C ( 1 , -4 ) , D ( -2 , 3 ) , E ( 0 , -8 ), F ( 1, 0 )$
These points can be plotted on the co - ordinate system as follows :
1819755_1855799_ans_dee00570ee8b464fa970e3f104e3d6b0.png

1819755_1855799_ans_dee00570ee8b464fa970e3f104e3d6b0.png

Plot points (-1,0),(1,0),(1,1),(0,2),(-1,1). Which figure is obtained by joining them serially.

Let points be

$P(-1,0), Q(1,0), R(1,1), S(0,2), T(-1,1)$ as shown in figure.
The figure generated is a "Pentagon".
1857441_1876325_ans_16b7e2a965564cb28cb9b6c822100512.png

In the following, which points lie on $y$ -axis $\mathrm{A}(1,1), \mathrm{B}(1,0), \mathrm{C}(0,1), \mathrm{D}(0,0), \mathrm{E}(-1,0), \mathrm{F}(0,-1), \mathrm{G}(4,0), \mathrm{H}(0,-7)$

On y-axis, x coordinate is zero of each point.

$\mathrm{C}(0,1), \mathrm{D}(0,0), \mathrm{F}(0,-1)$ and

$\mathrm{H}(0,-7)$ lie on

$\mathrm{y}$ -axis.

Draw a quadrilateral, if its vertices are following:
(-2,-2), (-4,2), (-6,-2) and (-4,-6)
Also mention the type of the obtained quadrilateral.

First draw two perpendicular axis XOX' and YOY', let the vertices of quadrilateral are

$P(-2,-2), Q(-4,2), R(-6,-2)$ and

$S(-4,-6)$
Plot these points of the coordinate axis as shown in the figure.
It is clear from the figure, It is clear from figure that

$PQ=QR=RS=ST$ . Hence given quadrilateral is rhombus.
1857483_1876344_ans_45af293674784b00b8cad579c6c46a4f.png

Draw the points $\mathrm{A}(4,4)$ and $\mathrm{B}(-4,4)$ and join $\mathrm{OA}, \mathrm{OB}$ and $\mathrm{AB},$ Name the figure made by such type.

Draw the points

$\mathrm{A}(4,4)$ and

$\mathrm{B}(-4,4)$ and join

$\mathrm{OA}, \mathrm{OB}$ and

$\mathrm{AB}$ . If is clear from figure it is a triangle.
Hence,

$\triangle \mathrm{OAB}$ is a equilateral triangle.
1860639_1877555_ans_78732eef650a47ca8c0a70179411214d.png

In the following, which points lie on $x$ -axis $\mathrm{A}(1,1), \mathrm{B}(1,0), \mathrm{C}(0,1), \mathrm{D}(0,0), \mathrm{E}(-1,0), \mathrm{F}(0,-1), \mathrm{G}(4,0), \mathrm{H}(0,-7)$

$x$ -axis, y coordinate is zero of each point,

$So B(1,0), D(0,0) E(-1,0)$ and

$G(4,0)$ lie on

$x$ -axis.

In which quadrant do each of the points (-2,4),(3,-1),(-1,0),(1,2) and (-3,-5) lie ? Verify, your answer by locating, then on the Cartesian plane

(i) Point

$(-2,4)$ lie in

$II$ quadrant
(ii) Point

$(3,-1)$ lie in

$IV$ quadrant
(iii) Point

$(-1,0)$ lie at negative x-axis
(iv) Point

$(1,2)$ lie at

$I$ quadrant
(v) Point

$(-3,-5)$ lie at III quadrant Position of all points are seen in the following Cartesian plane.
1860588_1877578_ans_bb35c7afb7874e11a17852f9a3fb52d1.png

1860588_1877578_ans_bb35c7afb7874e11a17852f9a3fb52d1.png

Plot P(2, 4) and Q(-2, 1). Reflect points P and Q in X-axis to get P' and Q'
(i) write their coordinates
(ii) give a geometrical name to the figure formed by joining the points PQQ'P'.

$\textbf{Step 1: Plot the given points.}$

$\text{The given points are P(2,4) and Q}(-2,1).$

$\text{These points are plotted on the graph.}$

$\textbf{Step 2: Reflect the given points.}$

$\text{Image of point P(2,4) reflected on X-axis is P'}(2,-4).$

$\text{Image of point Q}(-2,1)\text{ reflected on X-axis is Q'}(-2,-1).$

$\textbf{Step 3: Name the figure.}$

$\text{The figure PQQ'P' obtained by joining the points is a trapezium.}$

$\textbf{Hence, the image of the points are P'}\mathbf{(2,-4)}\textbf{ and Q'}\mathbf{(-2,-1)}\textbf{ respectively.}$

$\textbf{And the figure formed is a trapezium.}$

2173224_1985883_ans_3241558d3cf14869af731c48352b7590.PNG

Plot the points $(2, 4) and$ (4, 2) on a graph paper, and then draw a line segment joining these two points
Extend the line segment on both sides to meet the coordinate axis. What are the coordinates of the points where this line meets the x- axis and the y-axis?

1976542_1794558_ans_1a247647eb204da6bd2efb2f15b1fc67.jpeg

Find the quadrant in which the following point lie:
$A(7, -3)$

$A\left( { 7,-3 } \right)$ .

As the

$x$ co-ordinate is positive and

$y-$ co-ordinate is negative so the point lies in fourth quadrant.

1196549_1316415_ans_d5fe5d14cf2f4bdeb91a5ffd2fc1377d.png

In what ratio is the line segment joining $\left(-2,4\right)$ and $\left(-3,2\right)$ divided by the line $x-y=5?$

The given line is

$x-y=5$ ..........

$(1)$

Let the line

$(1)$ divide the line segment joining the point

$\left(-2,4\right)$ and

$\left(-3,2\right)$ at the point

$P$ in the ratio

$k:1$ then the co-ordinates of point

$P$ are

$\left(\dfrac{-3k-2}{k+1},\dfrac{2k+4}{k+1}\right)$

Since

$P$ lies on

$(1)$ , we get

$\dfrac{-3k-2}{k+1}-\dfrac{2k+4}{k+1}=5$

$\Rightarrow\,-3k-2-2k-4=5k+5$

$\Rightarrow\,-5k-6=5k+5$

$\Rightarrow\,-5k-5k=6+5$

$\Rightarrow\,-10k=11$

$\Rightarrow\,k=\dfrac{-11}{10}$

Hence, the required ratio is

$\dfrac{-11}{10}:1$ or

$11:10$ externally.

Coordinate Geometry - Class 9 Maths - Extra Questions

State to which quadrant does the following points belong:D(−3,2)D(-3, 2)

State to which quadrant does the following points belong:K(72,32)K\left(\dfrac{7}{2}, \dfrac{3}{2}\right)

State to which quadrant does the following points belong:Q(−5,−2)Q(-5, -2)

State to which quadrant does the following points belong:S(−4,5)S(-4, 5)

State to which quadrant does the following point belong: A(2,3)A(2, 3)(Enter the integer value to whichever quadrant it belongs to, For example for III quadrant enter 3)

State to which quadrant does the following points belong:U(−6.2,4.3)U(-6.2, 4.3)

In which quadrant (in number) or on which axis will (x,y)(x, y) lie if x>0x>0 and y<0y<0?

In which quadrant (in number) or on which axis will (x,y)(x, y) lie if x>0x>0 and y>0y>0?

In which quadrant (in number) or on which axis will (x,y)(x, y) lie if x<0x<0 and y>0y>0?

In which quadrant does the point lie if xx co-ordinate is positive and yy co-ordinate is negative ?

In which quadrant does the point lie if both the co-ordinates are positive?

In which quadrant does the point lie if both the co-ordinates are negative ?

State to which quadrant does the following points belong:L(3,−7)L(3, -7) (Enter the integer value to which ever quadrant it belongs to, For example for III quadrant enter 3)

State to which quadrant does the following points belong:M(−4,−1)M(-4, -1)

State to which quadrant does the following points belong:C(8,9)C(8, 9)

The yy-axis is the vertical number line.enter 1 for true and 0 for false

In which quadrant or on which axis will (x,y)(x, y) lie if x<0x<0 and y=0y=0?

In which quadrant or on which axis will (x,y)(x, y) lie if x=0x=0 and y>0y>0?

The origin (0,0)(0, 0) lies on the xx-axis.Answer 11 if True and 00 if False.

In which quadrant (in number) or on which axis will (x,y)(x, y) lie if x<0x<0 and y<0y<0?

By using graph, the quadrant (in number) in which (−2,5)(-2,5) lies is ____.

By using graph, (in numbers) find the quadrant or axis in which (3,−2)(3,-2) lies.

State true or false:The origin is in the first quadrant.

By using graph, the quadrant (in number) in which (3,6)(3,6) lies is ___ .

Plot the following point on a graph paper: (−4,−3)(-4, -3).

If (8,7)(8, 7) is plotted in correct place of graph then write answer is 1,1, else 00.

The point (a,b)(a, b) lies on the yy-axis if b=0b = 0.

If the ordinate of a point is equal to its abscissa; the point lies either in the first quadrant or in the second quadrant.

The y-axis is the vertical number line.If above statement is true then enter 11 and if false then enter 00.

The origin (0,0)(0, 0) lies on the xx-axis.

Every point is located in one of the four quadrants.

How will you describe the position of a table lamp on your study table to another person?

Which of the following points lies on the x-axis(i) (1,1)(1,1)(ii) (1,0)(1,0)(iii)(0,1)(0,1)(iv)(0,0)(0,0)(V)(−1,0)(-1,0)(vi)(0,−1)(0,-1)(vii)(4,0)(4,0)(viii)(0,−7)(0,-7)

Plot the points (x,y)(x,y) given in the following table on the plane, choosing suitable units of distance on the axes.xx -2 -1 01 3yy 87 -1.25 3 -1

In the diagram providedIf the coordinates of BB is (k,−2)(k,-2). Then the value of kk is

State the coordinates of S.

On the graph, plot the point X(8,−3)X (8, -3).

Which of the points shown below lies in the 3rd quadrant?A (-4, 2) B (4, 2) C (3, -5) D (-5, -2)

In the diagram, mark and label point S(15,4)S (15, 4).

On the graph, plot the point V(−4,10)V(-4, 10) .

State the coordinates of points A,B,CA, B, C and DD on the Cartesian plane below.

Based on the graph, state the coordinates of the point U.

Write the coordinates of points A,B,C,D,EA, B, C, D, E and FF on the Cartesian plane.

Fill in the blanks with suitable words:The yy-coordinate of a point on the xx-axis is _____________.

Find the quadrant in which (8,−100)(8,-100) lie

Find the quadrant in which (−800,−3000)(-800,-3000) lie

Find the quadrant in which the point (5,10)(5,10) lies in.

Find the quadrant in which (−8,9)(-8,9) lie

Draw the graph of yx=y+1x+2\cfrac{y}{x}=\cfrac{y+1}{x+2}

Suppose you are given a coordinate system. Determine the quadrant in which the following points lie:(i)(i) A(4,5)A(4,5); (ii)(ii) B(−4,−5)B(-4,-5); (iii)(iii) C(4,−5)C(4,-5).

Fill in the blanks with suitable words:If a point (x,y)≠(0,0)(x,y)\ne (0,0) is in the third quadrant, then (x+y)(x+y) has _________ sign.

Fill in the blanks with suitable words:The xx-axis and yy-axis intersect at ____________.

Write the coordinates of the points marked in graph.

Fill in the blanks with suitable words:If a point (x,y)(x,y) lies above horizontal axis, then yy is always __________.

State True or False:In a rectangular coordinate system, the coordinate axes are chosen such that they form a pair of perpendicular lines.

Plot the following point in the Cartesian plane.A(-5, -3)

Look at the graph. Write the coordinates of the points A,B,C,D,E,F,G,H,I,J,K,L,L,M,N,P,OA, B, C, D, E, F, G, H, I, J, K, L, L, M, N, P, O and QQ.

Write the following based on the graph.The abscissa of N is

Name the quadrant on which following point lies:(4,−2)(4, -2)

Plot the following point on the Cartesian plane.N(1,−6)N(1, -6)

Write the following based on the graph.The ordinate of Q is

x 23 -1 0 -9 -4 y -3 -3 4 11 0 -6 Plot the following points in the Cartesian plane whose x, y coordinates are given.

(-3, 5), (-1, 7)

Join the following pairs of point by a straight line segment, in the graph:(2, 5), (2, -4)

(-3, -5), (2, -5)

(-2, 1), (-2, 0)

(4, -2), (4, -3)

(-3, -4), (2, -4)

(-2, 4), (-2, 3)

Join the following pairs of point by straight line segment, in the graph:(-3, 2), (2, 2)

Join the following pairs of point by straight line segment, in the graph:(-3, 5), (-3, 4)

Join the following pairs of point by straight line segment, in the graph:(2, -4), (4, -2)

Draw the figure for an angle in the standard position. If the initial arm rotates through 80o{80}^{o} in the clockwise direction, then state the quadrant in which the terminal arm lies.

The terminal arm is in II (second) quadrant, what is the possible measure of an angle?

For the angle in standard position if the initial arm rotates 25o{25}^{o} in anti-clockwise direction, then state the quadrant in which the terminal arm lies.

Draw the figure for an angle in the standard position. If the initial arm rotates through 170o{170}^{o} in the clockwise direction, then state the quadrant in which the terminal arm lies.

Plot the following points on a graph paper and find out in which quadrant do they lie? (i) A (3,5) (ii) B (-2 , 7) (iii) C (-3,-5) (iv) D (2, -7) (v) O (0, 0)

Plot the point (4,5)(4, 5) on a graph sheet. Is it the same as (5,4)(5, 4) ?

Draw the figure for an angle in the standard position. If the initial arm rotates through 300o{300}^{o} in the clockwise direction, then state the quadrant in which the terminal arm lies.

State to which quadrant does the following points belong:
$D(-3, 2)$

State to which quadrant does the following points belong:
$K\left(\dfrac{7}{2}, \dfrac{3}{2}\right)$

State to which quadrant does the following points belong:
$Q(-5, -2)$

State to which quadrant does the following points belong:
$S(-4, 5)$

State to which quadrant does the following point belong: $A(2, 3)$

(Enter the integer value to whichever quadrant it belongs to, For example for III quadrant enter 3)

State to which quadrant does the following points belong:
$U(-6.2, 4.3)$

In which quadrant (in number) or on which axis will $(x, y)$ lie if $x>0$ and $y<0$ ?

In which quadrant (in number) or on which axis will $(x, y)$ lie if $x>0$ and $y>0$ ?

In which quadrant (in number) or on which axis will $(x, y)$ lie if $x<0$ and $y>0$ ?

$x$ co-ordinate is positive and $y$ co-ordinate is negative ?

State to which quadrant does the following points belong:
$L(3, -7)$ (Enter the integer value to which ever quadrant it belongs to, For example for III quadrant enter 3)

State to which quadrant does the following points belong:
$M(-4, -1)$

State to which quadrant does the following points belong:
$C(8, 9)$

The $y$ -axis is the vertical number line.
enter 1 for true and 0 for false

In which quadrant or on which axis will $(x, y)$ lie if $x<0$ and $y=0$ ?

In which quadrant or on which axis will $(x, y)$ lie if $x=0$ and $y>0$ ?

The origin $(0, 0)$ lies on the $x$ -axis.
Answer $1$ if True and $0$ if False.

In which quadrant (in number) or on which axis will $(x, y)$ lie if $x<0$ and $y<0$ ?

By using graph, the quadrant (in number) in which $(-2,5)$ lies is ____.

By using graph, (in numbers) find the quadrant or axis in which $(3,-2)$ lies.

State true or false:
The origin is in the first quadrant.

By using graph, the quadrant (in number) in which $(3,6)$ lies is ___ .

Plot the following point on a graph paper: $(-4, -3)$ .

If $(8, 7)$ is plotted in correct place of graph then write answer is $1,$ else $0$ .

The point $(a, b)$ lies on the $y$ -axis if $b = 0$ .

The y-axis is the vertical number line.
If above statement is true then enter $1$ and if false then enter $0$ .

The origin $(0, 0)$ lies on the $x$ -axis.

Which of the following points lies on the x-axis
(i) $(1,1)$
(ii) $(1,0)$
(iii) $(0,1)$
(iv) $(0,0)$
(V) $(-1,0)$
(vi) $(0,-1)$
(vii) $(4,0)$
(viii) $(0,-7)$

Plot the points $(x,y)$ given in the following table on the plane, choosing suitable units of distance on the axes.
$x$ -2 -1 0 1 3
$y$ 8 7 -1.25 3 -1

In the diagram provided
If the coordinates of $B$ is $(k,-2)$ . Then the value of $k$ is

On the graph, plot the point $X (8, -3)$ .

Which of the points shown below lies in the 3rd quadrant?
A (-4, 2) B (4, 2) C (3, -5) D (-5, -2)

In the diagram, mark and label point $S (15, 4)$ .

On the graph, plot the point $V(-4, 10)$ .

State the coordinates of points $A, B, C$ and $D$ on the Cartesian plane below.

Write the coordinates of points $A, B, C, D, E$ and $F$ on the Cartesian plane.

Fill in the blanks with suitable words:
The $y$ -coordinate of a point on the $x$ -axis is _____________.

Find the quadrant in which $(8,-100)$ lie

Find the quadrant in which $(-800,-3000)$ lie

Find the quadrant in which the point $(5,10)$ lies in.

Find the quadrant in which $(-8,9)$ lie

Draw the graph of $\cfrac{y}{x}=\cfrac{y+1}{x+2}$

Suppose you are given a coordinate system. Determine the quadrant in which the following points lie:
$(i)$ $A(4,5)$ ; $(ii)$ $B(-4,-5)$ ; $(iii)$ $C(4,-5)$ .

Fill in the blanks with suitable words:
If a point $(x,y)\ne (0,0)$ is in the third quadrant, then $(x+y)$ has _________ sign.

Fill in the blanks with suitable words:
The $x$ -axis and $y$ -axis intersect at ____________.

Fill in the blanks with suitable words:
If a point $(x,y)$ lies above horizontal axis, then $y$ is always __________.

State True or False:
In a rectangular coordinate system, the coordinate axes are chosen such that they form a pair of perpendicular lines.

Plot the following point in the Cartesian plane.
A(-5, -3)

Look at the graph. Write the coordinates of the points $A, B, C, D, E, F, G, H, I, J, K, L, L, M, N, P, O$ and $Q$ .

Write the following based on the graph.
The abscissa of N is

Name the quadrant on which following point lies:
$(4, -2)$

Plot the following point on the Cartesian plane.
$N(1, -6)$

Write the following based on the graph.
The ordinate of Q is

x 2 3 -1 0 -9 -4
y -3 -3 4 11 0 -6
Plot the following points in the Cartesian plane whose x, y coordinates are given.

Join the following pairs of point by a straight line segment, in the graph:
(2, 5), (2, -4)

Join the following pairs of point by straight line segment, in the graph:
(-3, 2), (2, 2)

Join the following pairs of point by straight line segment, in the graph:
(-3, 5), (-3, 4)

Join the following pairs of point by straight line segment, in the graph:
(2, -4), (4, -2)

Draw the figure for an angle in the standard position. If the initial arm rotates through ${80}^{o}$ in the clockwise direction, then state the quadrant in which the terminal arm lies.

For the angle in standard position if the initial arm rotates ${25}^{o}$ in anti-clockwise direction, then state the quadrant in which the terminal arm lies.

Draw the figure for an angle in the standard position. If the initial arm rotates through ${170}^{o}$ in the clockwise direction, then state the quadrant in which the terminal arm lies.

Plot the following points on a graph paper and find out in which quadrant do they lie?
(i) A (3,5) (ii) B (-2 , 7) (iii) C (-3,-5) (iv) D (2, -7) (v) O (0, 0)

Plot the point $(4, 5)$ on a graph sheet. Is it the same as $(5, 4)$ ?

Draw the figure for an angle in the standard position. If the initial arm rotates through ${300}^{o}$ in the clockwise direction, then state the quadrant in which the terminal arm lies.

Draw the line joining the following points.
P (-4,5) and Q (3,-4).

Drawing straight parallel lines to axes :
Draw the graph of x = 0.

$(-2, 8)$ point lies on ________ quadrant

Identify the quadrants of the points $A(2, 3), B(-2, 3), C(-2, -3)$ and $D(2, -3)$ . Discuss the type of the diagram by joining all the points.

Plot the following point in the rectangular coordinate system
$C(-2, -3)$

Plot the following point in the rectangular coordinate system.
$D(3, - 2)$

Plot the following point in the rectangular coordinate system.
$B(-4, 3)$

Plot the following point in the rectangular coordinate system.
$A(5, 4)$

Plot the points $(0, 4), (0, - 2), (0, 5)$ and $(0, -4)$ in the cartesian plane.

Plot the points $(-1, 0), (2, 0), (-5, 0)$ and $(4, 0)$ in the cartesian plane.

Plot the points (i) $(-1, 2)$ , (ii) $(-4, 2)$ , (iii) $(4, 2)$ and (iv) $(0, 2)$ . What can you say about the position of these points?

Write down the abscissa for the following point.
$(3, 5)$

On which axis do the following points lie?

(i) $P(5,0)$ (ii) $Q(0.-2)$ (iii) $R(-4,0)$ (iv) $S(0,5)$

Plot the following points. $A(0, 4), B(2, 3), C(1, 1)$ and $D(2, 0)$ .

Write down the ordinate of the following point.
$(-5, 8)$

Write down the ordinate of the following point:
$(7, 5)$