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CBSE - Class 10 Mathematics Coordinate geometry Worksheet

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

The point on x axis equidistant from I and E is

a.

(1/2, 0)

b.

(0,-1/2)

c.

(-1/2,0)

d.

(-1/2,0)

3.

Determine the ratio in which the straight line x-y-2=0 divides the line segment joining (3,-1) and (8,9).

4.
Prove that the point (3.0) (6,4) and (-1,3) are the vertices of a right angles isosceles triangle.
5.

 The points (-5, 1), (1, p) and (4, -2) are collinear if
the value of p is

a.

3

b.

2

c.

1

d.

-1

6.
If A and B are (– 2, – 2) and (2, – 4), respectively, find the coordinates of P such that AP = $\frac{3}{7}$ AB and P lies on the line segment AB.
7.

Find the point on the x-axis which is equidistant from the points (5,4) and (-2,3). Also find the area of triangle formed by points.

8.
If A(2,-1), B(3,4), C(-2,3) and D(-3,-2) be four points in a plane, show that ABCD is a rhombus but not a square.
9.

The area of the triangle formed by the points A(-1.5, 3), B(6, -2) and C(-3, 4) is

a.

0

b.

1

c.

2

d.

3/2

10.
If the point P(x,y) is equidistant from the points Q(a+b, b-a) and R(a-b, a+b), then prove that bx = ay.
11.
Show that A(-1, 0), B(3,1), C(2,2), D(-2,1) are the vertices of a parallelogram ABCD .
12.

In which quadrant does a point lie whose both coordinates are negative

a.

first quadrant

b.

second quadrant

c.

third quadrant

d.

Fourth quadrant

13.

true-false question ?

a. True b. False
14.

A hockey field is the playing surface for the game of hockey. Historically, the game was played on natural turf (grass) but nowadays it is predominantly played on an artificial turf. It is rectangular in shape - 100 yards by 60 yards. Goals consist of two upright posts placed equidistant from the centre of the backline, joined at the top by a horizontal crossbar. The inner edges of the posts must be 3.66 metres (4 yards) apart, and the lower edge of the crossbar must be 2.14 metres (7 feet) above the ground. Each team plays with 11 players on the field during the game including the goalie. Positions you might play include-  Forward: As shown by players A, B, C and D.  Midfielders: As shown by players E, F and G.  Fullbacks: As shown by players H, I and J.  Goalie: As shown by player K Using the picture of a hockey field below, answer the questions that follow:

 

Q1:The coordinates of the centroid of ΔEHJ are

a.

(-2/3, 1)

b.

(1,-2/3)

c.

(2/3,1)

d.

( -2/3,-1)

15.
Find the coordinates of the points of trisection of the line segment joining (4, –1) and (–2, –3).
16.
Find the ratio in which y-axis divides the line segment joining the points A (5,-6) and B(-1,-4). Also find the coordinates of point of division.
17.

If the average of X, 2X+5, X+6 and 45 is 29, whats is "X"

a.

15

b.

20

c.

24

d.

32

18.

Q4: The point on x axis equidistant from I and E is

a.

(1/2, 0)

b.

(0,-1/2)

c.

(-1/2,0)

d.

( 0,1/2)

19.
Find the distance between the following pairs of points : (i) (2, 3), (4, 1)
20.

The line segment joining the points A(3,2) and B(5,1) is divided at the point P in the ratio 1:2 and P lies on the line 3x-18y + k =0. Find the value of K.

Worksheet Answers

2.
Option A

3.

x-y-2=0 divides AB in the ratio of 2:3

4.
AB2 + CA2 = BC2, Pythagoras theorem is verified; right angles triangle.
5.
Option D

7.

12.5 sq. units

8.
All the four sides are equal
9.
Option A

10.
bx = ay
11.
Diagnosis bisect each other. Hence it is parallelogram.
12.
Option C
13.
Option A
14.
Option A

16.
y-axis is (0,-13/3)
17.
Option A
18.
Option A

20.

K =19

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