MCQ Questions for Class 9 Maths Coordinate Geometry Quiz 2

Any point on the

$x$ -axis is of the form:

0%
$(x, y)$
0%
$(0, y)$
0%
$(x, 0)$
0%
$(x, x)$

Explanation

In the

$xy$ -plane, any point on the

$x$ -axis will have

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

$x$ -axis is of the form

$(x,0)$ .

Therefore, option

$C$ is correct.

Which of the given points lie on

$y$ -axis?

$A (1, 1), B (1, 0), C (0, 1), D (0, 0), E (0, 1), F ( 1, 0), G (0, 5), H ( 7, 0), I (3, 3)$ .

0%
$B, D, F, H$
0%
$A, C, E, H$
0%
$C, D, E, G$
0%
$B, D, F, G$

Explanation

If a point is on

$y$ -axis , then the

$x$ co-ordinate of that point should be zero.

Here, the

$x$ -coordinate is zero at:

$C(0,1)$ ,

$D(0,0)$ ,

$E(0,1)$

and

$G(0,5)$ .

Therefore, these points lies on the

$y$ -axis.

Hence, option

$C$ is correct.

State whether the following statement is true or false:

Point

$\displaystyle \left ( 8,7 \right )$ lies in the first quadrant of the graph.

0%
True
0%
False

Explanation

We know, for the point $(x,y)$ ,

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, the point $(8,7)$ .

That is, $x$ is $8$ , which is positive and $y$ is $7$ , which is also positive.

Hence, the given point $(8,7)$ lies in the $I$ st quadrant.

Therefore, the statement is true.

Hence, option $A$ is correct.

Any point on the line

$y = x$ is of the form

0%
$(a, a)$
0%
$(0, a)$
0%
$(a, 0)$
0%
$(-a, a)$

Explanation

${\textbf{Step - 1: Plot and identify points in the Cartesian plane.}}$

${\text{The given equation is}}$ $x = y.$

${\text{So, if}}$ $x = 1$ ${\text{and}}$ $y = 1.$

${\text{If}}$ $x = -5$ ${\text{and}}$ $y = -5.$

${\text{If}}$ $x = 0$ ${\text{and}}$ $y = 0.$

${\textbf{Step - 2: By Induction.}}$

$x = a$ ${\text{and}}$ $y = a.$

${\text{So, any point P on the line}}$ $x = y$ ${\text{will be of the form}}$ $\text{P} (a, a).$

${\textbf{ Hence the correct option (A) (a, a).}}$

State whether True or False:

A point whose

$y$ -coordinate is zero and

$x$ -coordinate is

$5$ will lie on the

$y$ -axis.

0%
True
0%
False
0%
Ambiguous
0%
Data insufficient

Explanation

The given point has

$y$ -coordinate as zero and

$x$ -coordinate as

$5$ .

So, the point is

$(5,0)$ and it lies on

$x$ -axis and not

$y$ -axis.

Thus, the given statement is false.

Therefore, option

$B$ is correct.

State the following statement is True or False:

The coordinates of the origin are

$(0, 0)$ .

0%
True
0%
False

Explanation

We know, the point of intersection of

$x$ and

$y$ axes is called the origin.

Also,

$x$ -axis and

$y$ -axis intersects each other when

$x=0$ and

$y=0$ .

Therefore, its coordinate is

$(0,0)$ .

That is, the given statement is true.

Hence, option

$A$ is correct.

The points

$(- 5,2)$ and

$(2, - 5)$ lie in the :

0%
same quadrants
0%
II and III quadrants respectively
0%
II and IV quadrants respectively
0%
IV and III quadrants respectively

Explanation

$\therefore$ The point

$(-5,2)$ lies at quadrant

$II$ and point

$(2,-5)$ lies at quadrant

$IV$

Which of the following points lie on the negative side of

$x -$ axis ?

0%
$( - 4, 0)$
0%
$( - 3, 2)$
0%
$(0, - 4)$
0%
$(5, - 7)$

Explanation

The points

$(-4,0)$ and

$(-3,2)$ lie on the negative side of

$x$ -axis as the

$x$ -coordinate at the points is negative.

State whether True or False:

A point whose

$x$ -coordinate is zero and

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

$y$ -axis.

0%
True
0%
False
0%
Ambiguous
0%
Data insufficient

Explanation

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.

That is, the statement is true.

Therefore, option

$A$ is correct.

State true or false:

The point

$(a, b)$ lies on the

$y$ -axis if

$b= 0$ .

0%
True
0%
False
0%
Depends
0%
None

Explanation

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.

But here, given the point $(a,b)$ and $b=0$ .

Then, the point will be $(a,0)$ .

Clearly, the point lies on the $x$ -axis.

Hence, the given statement is false.

Therefore, option $B$ is correct

Choose the correct option for the following statement.

The origin is in the first quadrant.

0%
True
0%
False
0%
Ambiguous
0%
Data insufficient

The co-ordinates of the three vertices of a rectangle

$ABCD$ are given. By plotting the given points, find the co-ordinates of the fourth vertex:

$A(2,0), B(8,0)$ and

$C(8,4)$ .

0%
$(4,2)$
0%
$(8,0)$
0%
$(8,8)$
0%
$(2,4)$

Explanation

The given co-ordinates of the vertices of the rectangle

$ABCD$ are

$A(2,0),\ B(8,0),\ C(8,4)$ .

We need to plot

$D$ on the graph.

Since,

$ABCD$ is rectangle,

$\therefore$ The abscissa of

$D$ will be same as that of

$A$ and ordinate of

$D$ will be same as that of

$C$ .

$\therefore$ Co-ordinates of

$D$ are

$(2,4)$ .

Thus,

$D=(2,4)$ .

Hence, option

$D$ is correct.

The co-ordinates of the three vertices of a rectangle

$ABCD$ are given. By plotting the given points, find the co-ordinates of the fourth vertex:

$A(4,2), B(-2,2)$ and

$D(4,-2)$ .

0%
$(2, -2)$
0%
$(-2,-2)$
0%
$(2,2)$
0%
$(-2,2)$

Explanation

The given coordinates of the vertices of rectangle

$ABCD$ are

$A(4,2), B(-2,2), D(4,-2)$ .

We have to plot

$C$ on the graph.

Since

$ABCD$ is a rectangle, the abscissa of

$C$ will be that of

$B$ and the ordinate of

$D$ will be that of

$C$ .

Therefore, the coordinate of

$C$ will be

$(-2,-2)$ .

Hence, option

$B$ is correct.

Write the coordinates of the point of intersection of

$x$ - axis and

$y$ - axis.

0%
$(5, 0)$
0%
$(0, 5)$
0%
$(1, 1)$
0%
$(0, 0)$

Explanation

The coordinates of the point of intersection of

$x$ -axis and

$y$ -axis is

$(0,0)$ which is also known as origin.

Therefore, option

$D$ is correct.

The coordinates of the point of intersection of X-axis and Y-axis is (0,0)
State true or false.

0%
True
0%
False

State true or false

The positions of

$(5, -8)$ and

$(-8, 5)$ is same

0%
True
0%
False

Explanation

The positions of

$(5,-8)$ and

$(-8,5)$ are not same as the abscissa and ordinate of both the points are not equal. Hence,the given statement is false.

By using graph we find that the point P

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

0%
True
0%
False

Explanation

Given, $P(0,-4)$ .

Here, the $x$ -coordinate is $0$ and $y$ -coordinate is $-4$ .

We know, a point on the $x$ -axis has the form $(a,0)$ , where $a$ is any number.

But the given point is in the form $(0,a)$ and therefore lies on the $y$ -axis.

Therefore, the point $P(0,4)$ lies on the $y$ -axis and so, the given statement is false.

Hence, option $B$ is correct.

The co-ordinates of the three vertices of a rectangle

$ABCD$ are given. By plotting the given points, find the co-ordinates of the fourth vertex:

$A(-4,-6), C(6,0)$ and

$D(-4,0)$ .

0%
$(-6, - 6)$
0%
$(6,6)$
0%
$(6,-6)$
0%
$(-6,6)$

Explanation

The given co-ordinates of the vertices of the rectangle

$ABCD$ are

$A(-4,-6),\ C(6,0),\ D(-4,0)$ .

We need to plot

$B$ on the graph.

Since,

$ABCD$ is rectangle,

$\therefore$ The abscissa of

$B$ will be same as that of

$C$ and ordinate of

$B$ will be same as that of

$A$ .

$\therefore$ Co-ordinates of

$B$ are

$(6,-6)$ .

Hence, option

$C$ is correct.

The point

$(-3,2)$ belongs to Quadrant ____________

0%
$I$
0%
$II$
0%
$III$
0%
$IV$

Explanation

For the point

$(-3, 2)$ ,

$x$ -coordinate

$=-3$ is negative and

$y$ -coordinate

$= 2$ is positive.
Hence the point will lie in the

$II$ quadrant.

The point

$(-2,0)$ lies on:

0%
$+$ ve $x$ -axis
0%
$+$ ve $y$ -axis
0%
$-$ ve $x$ -axis
0%
$-$ ve $y$ -axis

Explanation

Given,

$(-2,0)$ .

Since the

$y$ -coordinate is

$0$ , the point clearly lies on

$x$ -axis.

Also, the

$x$ -coordinate

$-2$ being negative, the point lies on the negative

$x$ -axis.

Hence, option

$C$ is correct.

The point

$(3,0)$ lies on:

0%
$+$ ve $x$ -axis
0%
$+$ ve $y$ -axis
0%
$-$ ve $x$ -axis
0%
$-$ ve $y$ -axis

Explanation

Given,

$(3,0)$ .

Since the

$y$ -coordinate is

$0$ , the point clearly, lies on

$x$ -axis.
Also, the

$x$ -coordinate

$3$ being positive, the point lies on the positive

$x$ -axis.

Therefore, option

$A$ is correct.

The point

$(-2,-3)$ belongs to Quadrant _______________

0%
$I$
0%
$II$
0%
$III$
0%
$IV$

Explanation

For the point

$(-2, -3)$ , both the

$x$ -coordinate

$= -2$ and

$y$ -coordinate

$= -3$ are negative.
Hence the point will lie in the quadrant

$III$ .

The point

$(0,-2)$ lies on:

0%
$+$ ve $x$ -axis
0%
$+$ ve $y$ -axis
0%
$-$ ve $x$ -axis
0%
$-$ ve $y$ -axis

Explanation

Given,

$(0,-2)$ .

Since the

$x$ -coordinate is

$0$ , the point clearly lies on

$y$ -axis.
Also, the

$y$ -coordinate

$-2$ being negative, the point lies on the negative

$y$ -axis.

Therefore, option

$D$ is correct.

The coordinates of a point, which lies on

$y$ -axis and is at a distance of

$4$ units above

$x$ -axis is ____.

0%
$(0,4)$
0%
$(4,4)$
0%
$(4,0)$
0%
$(0,-4)$

Explanation

Let the required point be

$P$ .

Given, the point lies on

$y$ -axis.

Then, its abscissa is

$0$ or

$x = 0$ .

Also, given the point is at a distance of

$4$ units above the

$x$ -axis,

So, its ordinate will be

$+4$ .
Hence, the co-ordinates of the required point are

$(0,4)$ .

Therefore, option

$A$ is correct.

The coordinates of a point, which lies on

$x$ -axis and is at a distance of

$7$ units to the right of the origin is ____.

0%
$(-7,0)$
0%
$(0,7)$
0%
$(7,0)$
0%
$(0,-7)$

Explanation

Let the required point be $P$ .

Given, the point lies on $x$ -axis.

Then, its ordinate is $0$ or $y = 0$ .

Also, given the point is at a distance of $7$ units to the right of origin.

So, its abscissa will be $+7$ .
Hence, the co-ordinates of the required point are $(7,0)$ .

Therefore, option

$C$ is correct.

The coordinates of a point lies on

$y$ -axis and is at a distance of

$6$ units below

$x$ -axis is ______.

0%
$(6, 0)$
0%
$(-6, -6)$
0%
$(0, -6)$
0%
$(-6, 0)$

Explanation

Let the required point be $P$ .

Given, the point lies on $y$ -axis.

Then, its abscissa is $0$ or $x = 0$ .

Also, given the point is at a distance of $6$ units below the $x$ -axis,

So, its ordinate will be $-6$ .
Hence, the co-ordinates of the required point are $(0,-6)$ .

Therefore, option

$C$ is correct.

See figure and complete the following statements.

The x-coordinate and y-coordinate of the point

$M$ are _______ and _______ respectively. Hence the coordinate of

$M$ are

0%
$-3,4,(-3,4)$
0%
$-2,4,(-3,4)$
0%
$-3,2,(-3,4)$
0%
$3,4,(-3,4)$

Explanation

The point M is at a distance of 4 units from the x - axis and 3 units from the y - axis.

It lies in the II quadrant.
Hence, the abscissa or the x-coordinate is

$-3$ , ordinate or the y-coordinate is

$4$ .

The point M is

$(-3,4)$

The coordinates of a point, lies on

$x$ -axis and is at a distance of

$3$ units to the left of the origin is _____.

0%
$(-3,0)$
0%
$(0,0)$
0%
$(3,0)$
0%
$(0.3)$

Explanation

Let the required point be $P$ .

Given, the point lies on $x$ -axis.

Then, its ordinate is $0$ or $y = 0$ .

Also, given the point is at a distance of $3$ units to the left of the origin.

So, its abscissa will be $-3$ .
Hence, the co-ordinates of the required point are $(-3,0)$ .

Therefore, option

$A$ is correct.

In which quadrant will point

$(-3, -4)$ lie?

0%
$I$
0%
$II$
0%
$III$
0%
$IV$

Explanation

Both the abscissa and ordinate are negative. So, it will lie in

$III$ quadrant.

So, option

$C$ is correct.

If the point

$P$ lies on the line

$y = 7$ and has its abscissa equal to

$-2$ , then its coordinates are ______.

0%
$P = (7, 2).$
0%
$P = (7, -2).$
0%
$P = (-2, 7).$
0%
$P = (2, 7).$

Explanation

Let the required point be

$P$ .

Given, point

$P$ lies on the line

$y = 7$ and has its abscissa equal to

$-2$ .
We know, any point lying on the line

$y=7$ will always have its ordinate

$= 7$ .
Therefore, coordinates of

$P = (-2, 7)$ .

Hence, option

$C$ is correct.

CBSE Questions for Class 9 Maths Coordinate Geometry Quiz 2 - MCQExams.com

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Practice Class 9 Maths Quiz Questions and Answers

CBSE Questions for Class 9 Maths Coordinate Geometry Quiz 2 - MCQExams.com

0:0:1

Practice Class 9 Maths Quiz Questions and Answers

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