Coordinate Geometry — Practice

Question 1

Find the distance between the points (-5, 7) and (-1, 3).

Accepted Answer

4 root2 units

Question 2

Find the distance between the points (a, b) and (-a, -b).

Accepted Answer

2 root(a^2 + b^2)

Question 3

Verify whether the points (1, 5), (2, 3) and (-2, -1) are collinear.

Accepted Answer

They are not collinear

Question 4

Show that the points (-4, -7), (-1, 2), (8, 5) and (5, -4) taken in order are the vertices of a rhombus, and find its area.

Accepted Answer

All four sides are 3 root10 and the diagonals are unequal, so it is a rhombus of area 72 square units

Question 5

Name the type of quadrilateral formed by (-3, 5), (3, 1), (1, -3) and (-5, 1), giving reasons.

Accepted Answer

A parallelogram, and not a rectangle

Question 6

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

Accepted Answer

(-7, 0)

Question 7

Can you draw a triangle with vertices (1, 5), (5, 8) and (13, 14)? Give a reason.

Accepted Answer

No, because the three points are collinear

Question 8

Find the point which divides the line segment joining (-1, 7) and (4, -3) in the ratio 2 : 3.

Accepted Answer

(1, 3)

Question 9

Find the points of trisection of the line segment joining (4, -1) and (-2, -3).

Accepted Answer

(2, -5/3) and (0, -7/3)

Question 10

Find the ratio in which the line segment joining (-3, 10) and (6, -8) is divided by (-1, 6).

Accepted Answer

2 : 7

Question 11

Find the point A, where AB is the diameter of a circle whose centre is (2, -3) and B is (1, 4).

Accepted Answer

(3, -10)

Question 12

The line segment AB meets the coordinate axes at A and B. If P(3, 6) divides AB in the ratio 2 : 3, find the points A and B.

Accepted Answer

A(5, 0) and B(0, 15)

Question 13

Find the centroid of the triangle with vertices (6, 2), (0, 0) and (4, -7).

Accepted Answer

(10/3, -5/3)

Question 14

Find the area of the triangle whose vertices are (0, 0), (3, 0) and (0, 2).

Accepted Answer

3 square units

Question 15

Find the value of K for which the points (8, 1), (K, -4) and (2, -5) are collinear.

Accepted Answer

K = 3

Question 16

Find the area of the triangle formed by joining the midpoints of the sides of the triangle whose vertices are (0, -1), (2, 1) and (0, 3). Find the ratio of this area to the area of the given triangle.

Accepted Answer

1 square unit, and the ratio is 1 : 4

Question 17

Find the area of the quadrilateral whose vertices taken in order are (-4, -2), (-3, -5), (3, -2) and (2, 3).

Accepted Answer

28 square units

Question 18

Find the area of the triangle formed by (2, 3), (6, 3) and (2, 6) using Heron's formula.

Accepted Answer

6 square units

Question 19

Find the slope of the line passing through (3, -2) and (-6, -2).

Accepted Answer

0

Question 20

Find the slope of the line passing through (2a, 3b) and (a, -b).

Accepted Answer

4b/a

Question 21

Find the slope of the segment joining A(2, 1) and B(2, 6), and explain your answer.

Accepted Answer

The slope is undefined, because the line is parallel to the Y-axis

Practice — Coordinate Geometry

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