CBSE Questions for Class 11 Engineering Maths Straight Lines Quiz 9 - MCQExams.com

The points $$(3,0), (6,4)$$ and $$(-1,3)$$ are vertices of a right-angled  triangle. Show that it is an isosceles triangle.
  • True
  • False
If the points $$P(a,-11), Q(5,b), R(2,15)$$ and $$S(1,1)$$ are the vertices of a parallelogram $$ABCD$$, find the values of $$a$$ and $$b$$.
  • $$a=5,b=3$$
  • $$a=4,b=10$$
  • $$a=4,b=3$$
  • None of these
State true or false
Points $$( -2 , -1 ) , (1 , 0 )  , ( 4 , 3)$$  and $$( 1 , 2)$$  are the vertex of the parallelogram 
  • True
  • False
The area of the triangle with vertices at $$(-4, 1), (1, 2)(4, -3)$$ is
  • $$14$$
  • $$16$$
  • $$15$$
  • None of these
Prove that The lines $$ax + by + c=0$$ and $$Ax + By + C = 0$$ are perpendicular if $$aA + bB = 0$$.
  • True
  • False
The coordinates of the point where the line joining $$P(3, 4, 1)$$ and $$Q(5, 1, 6)$$ crosses the xy-plane are:
  • $$\left( { - {{13} \over 5}, - {{23} \over 5},0} \right)$$
  • $$\left( {{{13} \over 5},{{23} \over 5},0} \right)$$
  • $$\left( {{{13} \over 5}, - {{23} \over 5},0} \right)$$
  • $$\left( { - {{13} \over 5},{{23} \over 5},0} \right)$$
The area of the triangle whose vertices are (3,8), (-4,2) and (5,-1) is 
  • $$75 \ sq. units$$
  • $$37.5 \ sq. units$$
  • $$45 \ sq. units$$
  • $$22.5 \ sq. units$$
If $$(3,2)$$ and $$(-3,2)$$ are two vertices of an equilateral triangle which contains within it the origin, what are the coordinates of the third vertex ?
  • $$(2,2\sqrt{2})$$
  • $$(1,2\sqrt{2})$$
  • $$(0,-3\sqrt{3})$$
  • $$None\ of\ these$$
The curve $$y=ax^3+bx^2+cx+5$$ touches the x-axis at $$P(-2,0)$$ and cuts the y-axis at a point $$Q$$ where its gradient is $$3$$. Then the value of $${a,b,c} $$ is 
  • $$A=\dfrac{9}{2}$$, $$B=\dfrac{1}{2}$$, $$C=\dfrac{3}{5}$$
  • $$A=\dfrac{-1}{2}$$, $$B=\dfrac{-3}{4}$$, $$C=3$$
  • $$A=\dfrac{9}{2}$$, $$B=\dfrac{-3}{4}$$, $$C=3$$
  • $$A=\dfrac{-9}{2}$$, $$B=\dfrac{1}{2}$$, $$C=\dfrac{-3}{5}$$

Find the value of $$x$$ such that $$AB=BC$$ where the coordinates of A, B and C are $$(2,1)$$, $$(x,0)$$  and $$(-2,-1)$$ respectively.
  • $$1$$
  • $$2$$
  • $$-2$$
  • $$0$$
Find the value of $$x_i$$, if the distance between the points $$(x_i, 2)$$ and $$(3, 4)$$ is $$8$$.
  • $$3\pm 2\sqrt{15}$$
  • $$3\pm \sqrt{15}$$
  • $$2\pm 3\sqrt{15}$$
  • $$2\pm \sqrt{15}$$
The coordinates of a point on Y-axis which are at a distance of $$5\sqrt 2 $$ from the point $$P(3,-2,5)$$ is -
  • $$(0,6,0)$$ or $$(0,-2,0)$$
  • $$(0,-6,0)$$ or $$(0,2,0)$$
  • $$(0,4,0)$$ or $$(0,-4,0)$$
  • $$(0,5,0)$$ or $$(0,-5,0)$$
C is a point on the line segment joining A(-3, 4) and B (2, 1) such that AC = 2 BC then coordinates of C are
  • $$\left( {\dfrac{1}{3},2} \right)$$
  • $$\left( {2,\dfrac{1}{3}} \right)$$
  • $$\left( {2,7} \right)$$
  • $$\left( {7,2} \right)$$
Find the area of the triangle formed by joining the mid points of the sides of the triangle whose vertices are $$(0.-1), (2, 1) and (0, 3)$$
  • $$4$$
  • $$8$$
  • $$1$$
  • $$2$$
If $$Q(0, 1)$$ is equidistant from $$P(5, -3)$$ and $$R(x, 6)$$, find the values of x. Also find the distances QR and PQ.
  • PQ=QR=$$\sqrt { 41} $$
  • PQ=20, QR=$$\sqrt { 29 } $$
  • PQ= $$\sqrt { 29 } $$, QR= 20
  • PQ$$=\sqrt { 19 } $$, QR = 21
What is the y intercept of the line that is parallel to $$y=3x,$$ and which bisects the area of rectangle with corners at $$(0,0), (4,0) ,(4,2) $$ and $$(0,2)$$? 
  • $$ -7$$
  • $$-6$$
  • $$ -5$$
  • $$ -4$$
Find the area of the triangle whose vertices are $$(-5, -1), (3, -5), (5, 2)$$
  • $$31 sq$$ $$units$$
  • $$32sq$$ $$units$$
  • $$33 sq$$ $$units$$
  • $$\text{no triangle can be formed}$$
An aeroplane flying horizontally $$1$$, above the ground is observed at an elevation of $$60$$ and after $$10$$ seconds the elevation is observed to be $$30$$. The uniform speed of the aeroplane in $$/h$$ is-
  • $$240$$
  • $$240\sqrt { 3 } $$
  • $$60\sqrt { 3 } $$
  • None of these
The points $$A(a, 0), B(0, b), C(c, 0)$$ & $$D(0, d)$$ are such that $$ac=bd$$ & a, b, c, d are all non-zero. Then the  points.
  • Form a parallelogram
  • Do not lie on a circle
  • Form a trapezium
  • Are concyclic
Find the coordinates of the point equidistant from the points $$A(-2, -3), B(-1, 0)$$ and $$C(7, -6)$$.
  • $$(3, -3)$$
  • $$(-3, 3)$$
  • $$(-2, -3)$$
  • $$(-3, -3)$$
Distance between A(x, y) and B(-4, 7) is $$\sqrt{41}.$$ Find x and y, if A's ordinate is thrice of its abscissa.
  • $$(\frac{-12}{5},\frac{36}{5})$$
  • $$(1,\dfrac{12}{5})$$
  • $$\text{both a and b}$$ 
  • none
The ends of the base of an isosceles triangle are at $$(2a, 0)$$ and $$(0, a)$$ and one side is parallel to Y-axis. The equation of the other side is?
  • $$x+2y-a=0$$
  • $$x+2y=2a$$
  • $$3x+4y-4a=0$$
  • $$3x-4y+4a=0$$
If $$A(-2,1),B(2,3)$$ and $$C(-2,-4)$$ are three points, then the angle between $$BA$$ and $$BC$$ is:
  • $$\tan ^{ -1 }{ \left( \cfrac { 3 }{ 2 } \right) } $$
  • $$\tan ^{ -1 }{ \left( \cfrac { 2 }{ 3 } \right) } $$
  • $$\tan ^{ -1 }{ \left( \cfrac { 7 }{ 4 } \right) } $$
  • $$none\ of\ these$$
A straight line L through the point $$(3,-2)$$ is inclined at an angle $$60$$ to the line $$\sqrt { 3 } x+y=1$$. If L also intersects the x-axis, the equation of L is-
  • $$y+\sqrt { 3 }x+2-3\sqrt { 3 }=0$$
  • $$y-\sqrt { 3 }x+2+3\sqrt { 3 }=0$$
  • $$\sqrt { 3 } y-x+3+2\sqrt { 3 } =0$$
  • $$\sqrt { 3 } y+x-3+2\sqrt { 3 } =0$$
A straight line is drawn through the point $$p\ (2,3)$$ and is inclined at an angle of $$30^{o}$$ with the $$x-$$axis, the co-ordinates of two points on it at a distance of $$4$$ from $$p$$ is/are
  • $$\left(2+2\sqrt{3},5\right)$$, $$\left(2-2\sqrt{3},1\right)$$
  • $$\left(2+2\sqrt{3},5\right)$$, $$\left(2+2\sqrt{3},1\right)$$
  • $$\left(2-2\sqrt{3},5\right)$$, $$\left(2-2\sqrt{3},1\right)$$
  • $$none\ of\ these$$
The points given are $$(1, 1)$$, $$(-2, 7)$$ and $$(3, 3)$$.Find distance between the points.
  • $$\sqrt45,$$$$7,$$$$\sqrt{8}$$
  • $$\sqrt{10},7,8$$
  • $$\sqrt{3},1,2$$
  • None of the above
The points $$(a, b), (-a, -b), (b\sqrt{3}, -a\sqrt{3})$$ are the vertices of a triangle which is
  • Isosceles
  • Equilateral
  • Right angled
  • Scalene
A line passing through $$(3,4)$$ meets the axis $$\overline {OX} $$ and $$\overline {OY} $$ at $$A$$ and $$B$$ respectively. Find the minimum area of triangle OAB. 
  • $$12$$
  • $$10$$
  • $$24$$
  • $$6$$
If the vertices of a triangle are $$(1,2),(4,-6)$$ and $$(3,5)$$, then its area is
  • $$\cfrac{23}{2}$$ sq. units
  • $$\cfrac{25}{2}$$ sq. units
  • $$12$$ sq.unit
  • none of these
$$ABC$$ is an isosceles triangle. If the coordinates of the base are $$B(1,3)$$ and $$C(-2,7)$$, the coordinates of vertex $$A$$ can be
  • $$(1,6)$$
  • $$(-1/2,5)$$
  • $$(5/6,6)$$
  • none of these
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