## Chapter 16 – Co-ordinate Geometry Exercise Ex. 16A

Find the distance between the points:

(i) A(9,3) and B(15, 11)

(ii) A(7, -4) and B(-5, 1)

(iii) A(-6, -4) and B(9, -12)

(iv) A(1, -3) and B(4, -6)

(v) P(a + b, a – b) and Q(a – b, a + b)

(vi) P(a sin a, a cos a) and Q(a cos a, -a sin a)

(i) The given points are A(9,3) and B(15,11)

_{}

(ii) The given points are A(7,4) and B(-5,1)

_{}

(iii) The given points are A(-6, -4) and B(9,-12)

_{}

(iv) The given points are A(1, -3) and B(4, -6)

_{}

(v) The given points are P(a + b, a – b) and Q(a – b, a + b)

(vi) The given points are P(a sin a, a cos a) and Q(a cos a, – a sina)

_{}

_{}

Find the distance of each of the following points from the origin:

(i) A(5, -12)

(ii) B(-5, 5)

(iii) C(-4, -6)

(i) The given point is A(5, -12) and let O(0,0) be the origin

_{}

(ii) The given point is B(-5, 5) and let O(0,0) be the origin

_{}

(iii) The given point is C(-4, -6) and let O(0,0) be the origin

_{}

Find

all possible values of a for which the distance between the points A(a, -1)

and B(5, 3) is 5 units.

The

given points are A(a, -1) and B(5,3)

_{}

Find all possible values of y for which

the distance between the points A(2, -3) and B(10,

y) is 10 units.

Find the values of x for which the

distance between the points P(x, 4) and Q(9, 10) is

10 units.

If the point A(x, 2) is equidistant from

the points B(8, -2) and C(2, -2), find the value of

x. Also, find the length of AB.

If the point A(0,

2) is equidistant from the points B(3, p) and C(p,5),

find the value of p. Also, find the length of AB.

Find the point on the x-axis which is equidistant from the points (-2, 5) and (-2, 9).

Let any point P on x – axis is (x,0) which is equidistant from A(-2, 5) and B(-2, 9)

_{}

This is not admissible

Hence, there is no point on x – axis which is equidistant from A(-2, 5) and B(-2, 9)

Find points on the x – axis, each o f which is at a distance of 10 units from the point A(11, -8).

Let A(11, -8) be the given point and let P(x,0) be the required point on x – axis

Then,

_{}

Hence, the required points are (17,0) and (5,0)

Find the point on the y-axis which is

equidistant from the points A(6, 5) and B(-4, 3).

If the point P(x, y) is equidistant from

the points A(5, 1) and B(-1, 5), prove that 3x = 2y.

If P(x, y) is a point equidistant from the points A(6, -1) and B(2, 3). Show that x – y = 3

Let A(6, -1) and B(2,3) be the given point and P(x,y) be the required point, we get

_{}

Find the coordinates of the point equidistant from three given points A(5, 3), B(5, -5) and C(1, -5).

Let the required points be P(x,y), then

PA = PB = PC. The points A, B, C are (5,3), (5, -5) and (1, -5) respectively

_{}

Hence, the point P is (3, -1)

If the points A(4, 3) and B(x, 5) lie on

a circle with the centre O(2, 3), find the value of x.

If the point C(-2,

3) is equidistant from the points A(3, -1) and B(x, 8), find the values of x.

Also, find the distance BC.

If the point P(2,

2) is equidistant from the points A(-2, k) and B(-2k, – 3), find k. Also,

find the length of AP.

If the point (x, y) is equidistant from

the points (a + b, b – a) and (a – b, a + b), prove that bx

= ay.

Using the distance formula, show that the

given points are collinear.

(1, -1), (5, 2) and (9, 5)

Using the distance formula, show that the

given points are collinear.

(6, 9), (0, 1) and (-6, -7)

Using the distance formula, show that the

given points are collinear

(-1, -1), (2, 3) and (8, 11)

Using the distance formula, show that the

given points are collinear.

(-2, 5), (0, 1) and (2, -3).

Show that the points A(7,

10), B(-2, 5) and C(3, -4) are the vertices of an isosceles right triangle.

Show that the points A(3,

0), B(6, 4) and C(-1, 3) are the vertices of an isosceles right triangle.

If A(5, 2), B(2, -2) and C(-2, t) are the

vertices of a right triangle with ∠B = 90°, then find the value of t.

Prove that the points A(2,

4), B(2, 6) and C(2 +, 5) are the vertices of an equilateral triangle.

Show that the points (-3, -3), (3, 3) and

(-3, 3) are the vertices of an equilateral triangle.

Show that the points A(-5, 6), B(3, 0) and C(9, 8) are the vertices of isosceles triangle. Calculate its area.

Let A(-5,6), B(3,0) and C(9,8) be the given points. Then

_{}

_{}

Show that the points O(0, 0), A(3, _{}) and B(3, –_{}) are the vertices of an equilateral triangle. Find the area of this triangle.

_{}are the given points

_{}

Hence, DABC is equilateral and each of its sides being _{}

_{}

Show that the following points are the vertices of a square:

(i)A(3, 2), B(0, 5), C(-3, 2) and D(0, -1)

(ii)A(6, 2), B(2, 1), C(1, 5) and D(5, 6)

(iii)P(0, -2), Q(3, 1), R(0, 4) and S(-3, 1)

(i)The angular points of quadrilateral ABCD are A(3,2), B(0,5), C(-3,2) and D(0,-1)

Thus, all sides of quad. ABCD are equal and diagonals are also equal

Quad. ABCD is a square

(ii)Let A(6,2), B(2,1), C(1,5) and D(5,6) be the angular points of quad. ABCD. Join AC and BD

Thus, ABCD is a quadrilateral in which all sides are equal and the diagonals are equal.

Hence, quad ABCD is a square.

(iii)Let P(0, -2), Q(3,1), R(0,4) and S(-3,1) be the angular points of quad. ABCD

Join PR and QSD

_{ }

Thus, PQRS is a quadrilateral in which all sides are equal and the diagonals are equal

Hence, quad. PQRS is a square

Show that the points A(-3, 2), B(-5, -5), C(2, -3) and D(4, 4) are the vertices of a rhombus. Find the area of this rhombus.

Let A(-3,2), B(-5, -5), C(2, -3) and D(4,4) be the angular point of quad ABCD. Join AC and BD.

_{}

_{}

Thus, ABCD is a quadrilateral having all sides equal but diagonals are unequal.

Hence, ABCD is a rhombus

_{}

Show that the points A(3,

0), B(4, 5), C(-1, 4) and D(-2, -1) are the vertices of a rhombus. Find its

area.

Show that the points A(6,

1), B(8, 2), C(9, 4) and D(7, 3) are the vertices of a rhombus. Find its

area.

Show that the points A(2, 1), B(5, 2), C(6, 4) and D(3, 3) are the angular points of a parallelogram. Is this figure a rectangle?

Let A(2,1), B(5,2), C(6,4) and D(3,3) are the angular points of a parallelogram ABCD. Then

_{}

Diagonal AC Diagonal BD

Thus ABCD is not a rectangle but it is a parallelogram because its opposite sides are equal and diagonals are not equal

Show that A(1,

2), B(4, 3), C(6, 6) and D(3, 5) are the vertices of a parallelogram. Show

that ABCD is not a rectangle.

Show that the following points are the vertices of a rectangle:

(i)A(-4, -1), B(-2, -4), C(4, 0) and D(2, 3)

(ii)A(2, -2), B(14, 10), C(11, 13) and D(-1, 1)

(i)A(0, -4), B(6, 2), C(3, 5) and D(-3, -1)

(i) Let A(-4, -1), B(-2, -4), C(4, 0) and D(2, 3) are the vertices of quad. ABCD. Then

Thus, ABCD is a quadrilateral whose opposite sides are equal and the diagonals are equal

Hence, quad. ABCD is a rectangle.

(ii)Let A(2, -2), B(14, 10), C(11, 13) and D(-1, 1) be the angular points of quad. ABCD, then

_{}

Thus, ABCD is a quadrilateral whose opposite sides are equal and diagonals are equal.

Hence, quad. ABCD is rectangle.

(iii)Let A(0, -4), B(6,2), C(3,5) and D(-3,-1) are the vertices of quad. ABCD. Then

_{ }

Thus, ABCD is a quadrilateral whose opposite sides are equal and the diagonals are equal

Hence, quad. ABCD is a rectangle

## Chapter 16 – Co-ordinate Geometry Exercise Ex. 16B

Find the coordinates of the point which divides the join of A(-1, 7) and B(4, -3) in the ratio 2 : 3.

The end points of AB are A(-1,7) and B(4, -3)

_{}

Let the required point be P(x, y)

By section formula, we have

_{}

Hence the required point is P(1, 3)

Find the coordinates of the points which divides the join of A(-5, 11) and B(4, -7) in the ratio 7 : 2.

The end points of PQ are P(-5, 11) and Q(4, -7_

_{}

By section formula, we have

_{}

Hence the required point is (2, -3)

Points P, Q, R and S divide the line

segment joining the points A(1, 2) and R(6, 7) in

five equal parts. Find the coordinates of P, Q and R.

Points P, Q and R in that order are dividing a line segment joining A(1, 6) and B(5, -2) in four equal parts, find the coordinates of P, Q and R.

Points P, Q, R divide the line segment joining the points A(1,6) and B(5, -2) into four equal parts

_{}Point P divide AB in the ratio 1 : 3 where A(1, 6), B(5, -2)

Therefore, the point P is

_{}

Also, R is the midpoint of the line segment joining Q(3, 2) and B(5, -2)

_{}

The line segment joining the points A(3, -4) and B(1, 2) is trisected at the points P(p, -2) and _{}. Find the values of p and q.

Point P divides the join of A(3, -4) and B(1,2) in the ratio 1 : 2.

Coordinates of P are:

_{}

Find the coordinates of the midpoint of the line segment joining:

(i)A(3, 0) and B(-5, 4)

(ii)P(-11, -8) and Q(8, -2)

(i)The coordinates of mid – points of the line segment joining A(3, 0) and B(-5, 4) are _{}

(ii)Let M(x, y) be the mid – point of AB, where A is (-11, -8) and B is (8, -2). Then,

_{}

If (2, p) is the midpoint of the line segment joining the points A(6, -5) and B(-2, 11), find the value of p.

The midpoint of line segment joining the points A(6, -5) and B(-2, 11) is

_{}

Also, given the midpoint of AB is (2, p)

_{}p = 3

The midpoint of the line segment A(2a, 4) and B(-2, 3b) is C(1, 2a + 1). Find the value of a and b.

C(1, 2a + 1) is the midpoint of A(2a, 4) and B(-2, 3b)

_{}

The line segment joining A(-2, 9) and B(6, 3) is a diameter of a circle with centre C. Find the coordinates of C.

Let A(-2, 9) and B(6, 3) be the two points of the given diameter AB and let C(a, b) be the center of the circle

Then, clearly C is the midpoint of AB

By the midpoint formula of the co-ordinates,

_{}

Hence, the required point C(2, 6)

Find

the coordinates of a point A, where AB is a diameter of a circle with centre

C(2, -3) and the other end of the diameter is B(1, 4).

A,

B are the end points of a diameter. Let the coordinates of A be (x, y)

The

point B is (1, 4)

The

center C(2, -3) is the midpoint of AB

_{}

The

point A is (3, -10)

In what ratio does the point P(2, 5) divide the join of A(8, 2) and B(-6, 9)?

Let P divided the join of A(8, 2), B(-6, 9) in the ratio k : 1

By section formula, the coordinates of p are

_{}

Hence, the required ratio of _{} which is (3 : 4)

Find the ratio in which the point P(m, 6) divides the join of A(-4, 3) and B(2, 8). Also, find the value of m.

Let P divided the join of line segment A(-4, 3) and B(2, 8) in the ratio k : 1

_{} the point P is

_{}

Find the ratio in which the point (-3, k) divides the join of A(-5, -4) and B(-2, 3). Also, find the value of k.

Let P is dividing the given segment joining A(-5, -4) and B(-2, 3) in the ratio r : 1

_{} Coordinates of point P

_{ }

In what ratio is the line segment joining A(2, -3) and B(5, 6) divided by the x-axis? Also, find the coordinates of the point of division.

Let the x- axis cut the join of A(2, -3) and B(5, 6) in the ratio k : 1 at the point P

Then, by the section formula, the coordinates of P are _{}

But P lies on the x axis so, its ordinate must be 0

_{}

So the required ratio is 1 : 2

Thus the x – axis divides AB in the ratio 1 : 2

Putting _{} we get the point P as

_{}

Thus, P is (3, 0) and k = 1 : 2

In what ratio is the line segment joining the points A(-2, -3) and B(3, 7) divided by the y-axis? Also, find the coordinates of the point of division.

Let the y – axis cut the join A(-2, -3) and B(3, 7) at the point P in the ratio k : 1

Then, by section formula, the co-ordinates of P are

_{}

But P lies on the y-axis so, its abscissa is 0

_{}

So the required ratio is _{} which is 2 : 3

Putting _{} we get the point P as

_{} i.e., P(0, 1)

Hence the point of intersection of AB and the y – axis is P(0, 1) and P divides AB in the ratio 2 : 3

In what ratio does the line x – y – 2 = 0 divide the line segment joining the points A(3, -1) and B(8, 9)?

Let the line segment joining A(3, -1) and B(8, 9) is divided by x – y – 2 = 0 in ratio k : 1 at p

_{} Coordinates of P are

_{}

Thus the line x – y – 2 = 0 divides AB in the ratio 2 : 3

Find the lengths of the medians of a _{}ABC whose vertices are A(0, -1), B(2, 1) and C(0, 3).

Let D, E, F be the midpoint of the side BC, CA and AB respectively in ABC

Then, by the midpoint formula, we have

_{}

Hence the lengths of medians AD, BE and CF are given by

_{}

Find the centroid of ABC whose vertices are A(-1, 0), B(5, -2) and C(8, 2).

Here _{}

Let G(x, y) be the centroid of ABC, then

_{}

Hence the centroid of ABC is G(4, 0)

If G(2, -1) is the centroid of a ABC and two of its vertices are A(1, -6) and B(-5,2), find the third vertex of the triangle.

Two vertices of ABC are A(1, -6) and B(-5, 2) let the third vertex be C(a, b)

Then, the co-ordinates of its centroid are

_{}

But given that the centroid is G(-2, 1)

_{}

Hence, the third vertex C of ABC is (-2, 7)

Find the third vertex of a ABC if two of its vertices are B(-3, 1) and C(0, -2), and its centroid is at the origin.

Two vertices of ABC are B(-3, 1) and C(0, -2) and third vertex be A(a, b)

Then the coordinates of its centroid are

_{}

Hence the third vertices A of ABC is A(3, 1)

Show that the points A(3, 1), B(0, -2), C(1, 1) and D(4, 4) are the vertices of a parallelogram ABCD.

Let A(3,1), B(0, -2), C(1, 1) and D(4, 4) be the vertices of quadrilateral

Join AC, BD. AC and BD, intersect other at the point O.

We know that the diagonals of a parallelogram bisect each other

Therefore, O is midpoint of AC as well as that of BD

Now midpoint of AC is _{}

And midpoint of BD is _{}

Mid point of AC is the same as midpoint of BD

Hence, A, B, C, D are the vertices of a parallelogram ABCD

If the points P(a, -11), Q(5, b), R(2, 15) and S(1, 1) are the vertices of a parallelogram PQRS, find the values of a and b.

Let P(a, -11), Q(5, b), R(2, 15) and S(1, 1) are the vertices of a parallelogram PQRS.

Join the diagonals PR and SQ.

They intersect each other at the point O. We know that the diagonals of a parallelogram bisect each other.

Therefore, O is the midpoint of PR as well as that of SQ

Now, midpoint of PR is _{}

And midpoint of SQ is _{}

_{}

Hence the required values are a = 4 and b = 3

If three consecutive vertices of a parallelogram ABCD are A(1, -2), B(3, 6) and C(5, 10), find the fourth vertex D.

Let A(1, -2), B(3, 6) and C(5, 10) are the given vertices of the parallelogram ABCD

Let D(a, b) be its fourth vertex. Join AC and BD.

Let AC and BD intersect at the point O.

We know that the diagonals of a parallelogram bisect each other.

So, O is the midpoint AC as well as that of BD

Midpoint of AC is _{}

Midpoint of BD is _{}

_{}

Hence the fourth vertices is D(3, 2)

In what ratio does y-axis divide the line

segment joining the points (-4, 7) and (3, -7)?

If the point Plies on the line segment joining the points A(3,

-5) 2 and B(-7, 9) then find the ratio in which P divides AB. Also, find the

value of y.

Find the ratio in which the line segment

joining the points A(3, -3) and B(-2, 7) is divided

by x-axis. Also, find the point of division.

The base QR of an equilateral triangle

PQR lies on x-axis. The coordinates of the point Q are (-4, 0) and origin is

the midpoint of the base. Find the coordinates of the points P and R.

The base BC of an equilateral triangle

ABC lies on y-axis. The coordinates of point C are (0, -3). The origin is the

midpoint of the base. Find the coordinates of the points A and B. Also, find

the coordinates of anther point D such that ABCD is a rhombus.

Find the ratio in which the points p(-1, y) lying on the line segment joining points A(-3, 10) and B(6, -8)

divides it. Also, find the value of y.

ABCD is a rectangle formed by the points A(-1, -1), B(-1, 4), C(5, 4) and D(5, -1). If P, Q, R and

S be the midpoints of AB, BC, CD and DA respectively, show that PQRS is a rhombus.

The midpoint P of the line segment

joining the points A(-10, 4) and B(-2, 0) lies on

the line segment joining the points C(-9, -4) and D(-4, y). Find the ratio in

which P divides CD. Also find the value of y.

## Chapter 16 – Co-ordinate Geometry Exercise Ex. 16C

Find the area of ABC, whose vertices are:

(i) A(1, 2), B(-2, 3) and C(-3, -4)

(ii) A(-5, 7), B(-4, -5) and C(4, 5)

(iii) A(3, 8), B(-4, 2) and C(5, -1)

(iv) A(10, -6), B(2, 5) and C(-1, 3)

(i) Let A(1, 2), B(-2, 3) and C(-3, -4) be the vertices of the given ABC, then

(ii) The coordinates of vertices of ABC are A(-5, 7), B(-4, -5) and C(4, 5)

Here, _{}

_{}

(iii) The coordinates of ABC are A(3, 8), B(-4, 2) and C(5, -1)

_{ }

(iv) Let P(10, -6), Q(2, 5) and R(-1, 3) be the vertices of the given PQR. Then,

_{}

Find the area of quadrilateral ABCD whose

vertices are A(3, -1), B(9, -5), C(14, 0) and D(9 -19).

Find the area of quadrilateral PQRS whose

vertices are P(-5, -3), Q(4, -6), R(2, -3) and S(1,

2).

Find the area of quadrilateral ABCD whose

vertices are A(-3, -1), B(-2, -4), C(4, -1) and D(3,

4).

Find the area of quadrilateral ABCD whose

vertices are A(-5, 7), B(-4, -5), C(-1, -6) and D(4,

5).

Find the area of the triangle formed by

joining the midpoints of the sides of the triangle whose vertices are A(2, 1), B(4, 3) and C(2, 5).

A(7, -3), B(5, 3) and C(3, -1) are

the vertices of a ∆ABC and AD is its median. Prove that the median AD divides

∆ABC into two triangles of equal areas.

Find the area of ∆ABC with A(1, -4) and midpoints of sides through A being (2, -1)

and (0, -1).

A(6, 1), B(8, 2) and C(9, 4) are

the vertices of a parallelogram ABCD. If E is the midpoint of DC, find the

area of ∆ADE.

If the vertices of ∆ABC be A(1, -3), B(4,

p) and C(-9, 7) 15 square units, find the values of p.

Find the value of k so that the area of

the triangle with vertices A(k + 1, 1), B(4, -3) and

C(7, -k) is 6 square units.

For what value of k(k

> 0) is the area of the triangle with vertices (-2, 5), (k, -4) and (2k +

1, 10) equal to 53 square units?

Show that the following points are

collinear.

A(2, -2), B(-3, 8) and C(-1, 4)

Show that the following points are

collinear.

A(-5, 1), B(5, 5) and C(10, 7)

Show that the following points are collinear.

A(5, 1), B(1, -1) and C(11, 4)

Show that the following points are

collinear.

A(8, 1), B(3, -4) and C(2, -5)

Find the value of x for which the points

A(x, 2), B(-3, -4) and C(7, -5) are collinear.

For what value of x are the points A(-3, 12), B(7, 6) and C(x, 9) collinear?

The given points are A(-3, 12), B(7, 6) and C(x, 9)

_{}

For what value of y are the points P(1, 4), Q(3, y) and R(-3, 16) collinear?

Let P(1, 4), Q(3, y) and R(-3, 16)

_{}

Find the value of y for which the points A(-3, 9), B(2, y) and C(4, -5) are collinear.

For what values of k are the points A(8, 1), B(3, -2k) and C(k, -5) collinear.

Find a relation between x and y, if the points A(2, 1), B(x, y) and C(7, 5) are collinear.

Vertices of _{}ABC are A(2, 1), B(x, y) and C(7, 5)

_{}

The points A, B and C are collinear

_{}area of _{}ABC =0

Or 4x – 5y – 3 = 0

Find a relation between x and y, if the

points A(x, y), B(-5,7) and C(-4, 5) are collinear.

Prove that the points A(a, 0), B(0, b) and C(1, 1) are collinear, if _{}.

The vertices of ABC are (a, 0), (0, b), C(1, 1)

_{}

The points A, B, C are collinear

_{}Area of ABC = 0

_{}ab – a – b = 0 _{}a + b = ab

Dividing by ab

_{}

If the points P(-3,

9), Q(a, b) and R(4, -5) are collinear and a + b = 1. find the values of a

and b.

Find the area of ∆ABC with vertices A(0, -1), B(2, 1) and C(0, 3). Also, find the area of the triangle

formed by joining the midpoints of its sides. Show that the ratio of the

areas of two triangles is 4 :1.

## Chapter 16 – Co-ordinate Geometry Exercise Ex. 16D

Points A(-1, y)

and B(5, 7) lie on a circle with centre O(2, -3y). Find the values of y.

If the point A(0, 2) is equidistant from

the points B(3, p) and C(p, 5), find p.

ABCD is a rectangle whose three vertices

are B(4, 0), C(4, 3) and D(0, 3). Find the length of

one of its diagonal.

If the point P(k – 1, 2) is equidistant

from the points A(3, k) and B(k, 5), find the values of k.

Find the ratio in which the point P(x, 2)

divides the join of A(12, 5) and B(4, -3).

Prove that the diagonals of a rectangle

ABCD with vertices A(2, -1), B(5, -1), C(5, 6) and

D(2, 6) are equal and bisect each other.

Find the lengths of the medians AD and BE

of ∆ABC whose vertices are A(7, -3), B(5, 3) and

C(3, -1).

If the point C(k, 4) divides the join of

A(2, 6) and B(5, 1) in the ratio 2 : 3 then find the value of k.

Find the point on x-axis which is

equidistant from points A(-1, 0) and B(5, 0).

Find the distance between the points _{}.

Distance between the points _{}

_{ }

Find the value of a, so that the point

(3, a) lies on the line represented by 2x – 3y = 5.

If the points A(4, 3) and B(x, 5) lie on the circle with centre O(2, 3), find the value of x.

The points A(4,3) and B(x, 5) lie on the circle with center O(2,3)

OA and OB are radius of the circle.

_{}

If P(x, y) is equidistant from the points A(7, 1) and B(3, 5), find the relation between x and y.

The point P(x, y) is equidistant from the point A(7, 1) and B(3, 5)

_{}

If the centroid of _{}ABC having vertices A(a, b), B(b, c) and C(c, a) is the origin, then find the value of (a + b + c).

The vertices of _{}ABC are (a, b), (b, c) and (c, a)

Centroid is _{}

But centroid is (0, 0)

a + b + c = 0

Find the centroid of _{}ABC whose vertices are A(2, 2), B(-4, -4) and C(5, -8).

The vertices of _{}ABC are A(2, 2), B(-4, -4) and C(5, -8)

Centroid of _{}ABC is given by

_{}

In what ratio does the point C(4, 5) divide the join of A(2, 3) and B(7 , 8)?

Let the point C(4, 5) divides the join of A(2, 3) and B(7, 8) in the ratio k : 1

The point C is _{}

But C is (4, 5)

_{}

Thus, C divides AB in the ratio 2 : 3

If the points A(2, 3), B(4, k)and C(6, -3) are collinear, find the value of k.

The points A(2, 3), B(4, k) and C(6, -3) are collinear if area of _{}ABC is zero

_{}

But area of ABC = 0,

_{}k = 0

## Chapter 16 – Co-ordinate Geometry Exercise MCQ

The distance of the point P(-6,8) from the origin is

The distance of the point (-3, 4) from x-axis is

(a) 3

(b) -3

(c) 4

(d) 5

The point on x-axis which is equidistant from points

A(-1, 0) and B(5, 0) is

(a) (0, 2)

(b) (2, 0)

(c) (3, 0)

(d) (0, 3)

If R(5, 6) is the midpoint of the line segment AB joining the points A(6, 5) and B(4, y) they y equals

(a) 5

(b) 7

(c) 12

(d) 6

If the point C(k, 4) divides the join of the points A(2, 6) and B(5,1) in the ratio 2:3 then the value of k is

The perimeter of the triangle with vertices (0, 4), (0, 0) and (3, 0) is

Correct option: (d)

If A(1, 3), B(-1, 2), C(2, 5) and D(x, 4) are the vertices of a ‖gm ABCD then the value of x is

Correct option: (b)

If the points A(x, 2), B(-3, -4) and C(7, -5) are collinear then the value of x is

(a) -63

(b) 63

(c) 60

(d) -60

The area of a triangle with vertices A(5, 0), B(8, 0) and C(8,4) in square units is

(a) 20

(b) 12

(c) 6

(d) 16

The area of ABC with vertices A(a, 0), O(0, 0) and

B(0, b) in square units is

(a) -8

(b) 3

(c) -4

(d) 4

ABCD is a rectangle whose three vertices are B(4, 0), C(4, 3) and D(0, 3). The length of one of its diagonals is

(a) 5

(b) 4

(c) 3

(d) 25

Correct option: (a)

The coordinates of the point P dividing the line segment joining the points A(1, 3) and B(4, 6) in the ratio 2:1 is

(a) (2, 4)

(b) (3, 5)

(c) (4, 2)

(d) (5, 3)

If the coordinates of one end of a diameter of a circle are (2, 3) and the coordinates of its centre are (-2, 5), then the coordinates of the other end of the diameter are

(a) (-6, 7)

(b) (6, -7)

(c) (4, 2)

(d) (5, 3)

In the given figure P(5, -3) and Q(3, y) are the points of trisection of the line segment joining A(7, -2) and

B(1, -5). Then y equals

The midpoint of segment AB is P(0, 4). If the coordinates of B are (-2, 3), then the coordinates of A are

(a) (2, 5)

(b) (-2, -5)

(c) (2, 9)

(d) (-2, 11)

The point P which divides the line segment joining the points A(2, -5) and B(5, 2) in the ratio 2:3 lies in the quadrant

(a) I

(b) II

(c) III

(d) IV

If A(6, -7) and B(-1, -5) are two given points then the distance 2AB is

(a) 13

(b) 26

(c) 169

(d) 238

Which point on x-axis is equidistant from the points

A(7, 6) and B(-3, 4)?

(a) (0, 4)

(b) (-4, 0)

(c) (3, 0)

(d) (0, 3)

The distance of P(3, 4) from the x-axis is

(a) 3 units

(b) 4 units

(c) 5 units

(d) 1 units

In what ratio does the x-axis divide the join of A(2, -3) and B(5, 6)?

(a) 2:3

(b) 3:5

(c) 1:2

(d) 2:1

In what ratio does the y-axis divide the join of P(-4, 2) and Q(8, 3)?

(a) 3:1

(b) 1:3

(c) 2:1

(d) 1:2

If P(-1, 1) is the midpoint of the line segment joining

A(-3, b) and B(1, b + 4) then b =?

(a) 1

(b) -1

(c) 2

(d) 0

The line 2x + y – 4 = 0 divides the line segment joining A(2, -2) and (3, 7) in the ratio

(a) 2:5

(b) 2:9

(c) 2:7

(d) 2:3

If A(4, 2), B(6, 5) and C(1,4) be the vertices of ∆ABC and AD is a median, then the coordinates of D are

If A(-1, 0), B(5, -2) and C(8,2) are the vertices of a ∆ABC then its centroid is

(a) (12, 0)

(b) (6, 0)

(c) (0, 6)

(d) (4, 0)

Two vertices of ∆ABC are A (-1, 4) and B(5, 2) and its centroid is G(0, -3). Then, the coordinates of are

(a) (4, 3)

(b) (4, 15)

(c) (-4, -15)

(d) (-15, -4)

The points A(-4, 0), B(4, 0) and C(0,3) are the vertices of a triangle, which is

(a) isosceles

(b) equilateral

(c) scalene

(d) right-angled

The point P(0, 6), Q(-5, 3) and R(3, 1)are the vertices of a triangle, which is

(a) equilateral

(b) isosceles

(c) scalene

(d) right-angled

If the points A(2, 3), B(5, k) and C(6, 7) are collinear then

If the point A (1, 2), O(0, 0) and C(a, b) are collinear then

(a) a = b

(b) a = 2b

(c) 2a = b

(d) a + b = 0

The area of ∆ABC with vertices A(3, 0), B(7, 0) and

C(8, 4) is

(a) 14 sq units

(b) 28 sq units

(c) 8 sq units

(d) 6 sq units

AOBC is a rectangle whose three vertices are A(0, 3), O(0, 0) and B(5, 0). The length of each of its diagonals is

If the distance between the points A(4, p) and B(1, 0) is 5 then

(a) p = 4 only

(b) p = -4 only

(c) p = ± 4

(d) p = 0