### CBSE 10 Mathematics Coordinate Geometry

### Practice Paper 05

1. Find the distance between the following pairs of points :

(i) (3, 5), (5, 1) (ii) (– 4, 5), (– 1, 2) (iii) (x, y), (– x, – y)

2. Find the values of y for which the distance between the points P(3, – 3) and Q(7, y) is 12 units.

3. Show that the points (1, 7), (4, 2), (–1, –1) and (– 4, 4) are the vertices of a square.

4. Find a relation between x and y such that the point (x , y) is equidistant from the points (7, 1) and (3, 5).

5. If Q(0, 1) is equidistant from P(4, –3) and R(x, 5), find the values of x. Also find the distances QR and PR.

6. Find a relation between x and y such that the point (x, y) is equidistant from the point (3, 5) and (– 3, 5).

7. Find the coordinates of the point which divides the line segment joining the points (4, – 3) and (8, 5) in the ratio 3 : 1 internally.

8. Find the coordinates of the points of trisection (i.e., points dividing in three equal parts) of the line segment joining the points A(2, – 2) and B(– 7, 4).

9. If the points A(6, 1), B(8, 2), C(9, 4) and D(p, 3) are the vertices of a parallelogram, taken in order, find the value of p.

10. Find the area of a rhombus if its vertices are (3, 0), (4, 5), (– 1, 4) and (– 2, – 1) taken in order.