Vardaan Learning Institute

Chapter Practice Sheet: Coordinate Geometry

Class: 10 (CBSE) Subject: Mathematics Max. Marks: 50
SECTION A: OBJECTIVE TYPE QUESTIONS (1 Mark Each)
1. The distance of the point P(2, 3) from the x-axis is:
  1. 2
  2. 3
  3. 1
  4. 5
[1]
2. The points (-1, -2), (1, 0), (-1, 2), (-3, 0) form a quadrilateral of type:
  1. Square
  2. Rectangle
  3. Parallelogram
  4. Rhombus
[1]
3. If the distance between the points (4, p) and (1, 0) is 5, then the value of p is:
  1. 4 only
  2. $\pm 4$
  3. -4 only
  4. 0
[1]
4. The mid-point of the line segment joining the points A(-2, 8) and B(-6, -4) is:
  1. (-4, -6)
  2. (2, 6)
  3. (-4, 2)
  4. (4, 2)
[1]
5. The point which divides the line segment joining the points (7, -6) and (3, 4) in the ratio 1:2 internally lies in the:
  1. I quadrant
  2. II quadrant
  3. III quadrant
  4. IV quadrant
[1]
6. If the points A(1, 2), B(0, 0) and C(a, b) are collinear, then:
  1. a = b
  2. a = 2b
  3. 2a = b
  4. a = -b
[1]
7. The distance of the point P(-6, 8) from the origin is:
  1. 8
  2. 2$\sqrt{7}$
  3. 10
  4. 6
[1]
8. If the mid-point of the line segment joining the points P(6, b-2) and Q(-2, 4) is (2, -3), find the value of b.
  1. -4
  2. -8
  3. 4
  4. 8
[1]
9. The coordinates of the point which divides the line segment joining (-1, 3) and (4, -7) internally in the ratio 3:2 are:
  1. (2, -3)
  2. (-2, 3)
  3. (2, 3)
  4. (-2, -3)
[1]
10. Assertion (A): The point (0, 6) lies on the y-axis.
Reason (R): The x-coordinate of every point on the y-axis is zero.
  1. Both A and R are true and R is the correct explanation of A.
  2. Both A and R are true but R is not the correct explanation of A.
  3. A is true but R is false.
  4. A is false but R is true.
[1]
SECTION B: SHORT ANSWER TYPE QUESTIONS (2 Marks Each)
11. Find the relations between x and y such that the point (x, y) is equidistant from the points (7, 1) and (3, 5).
[2]
12. Find the ratio in which the y-axis divides the line segment joining the points (5, -6) and (-1, -4). Also find the point of intersection.
[2]
13. 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]
14. Check whether (5, -2), (6, 4) and (7, -2) are the vertices of an isosceles triangle.
[2]
SECTION C: SHORT ANSWER TYPE II QUESTIONS (3 Marks Each)
15. Find the area of the rhombus if its vertices are (3, 0), (4, 5), (-1, 4) and (-2, -1) taken in order.
[3]
16. Find the coordinates of the points of trisection of the line segment joining (4, -1) and (-2, -3).
[3]
17. 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.
[3]
18. Find the ratio in which the line $2x + 3y - 5 = 0$ divides the line segment joining the points (8, -9) and (2, 1). Also find the coordinates of the point of division.
[3]
19. 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.
[3]
20. If the point C(-1, 2) divides internally the line segment joining A(2, 5) and B(x, y) in the ratio 3:4, find the coordinates of B.
[3]
SECTION D: LONG ANSWER TYPE QUESTIONS (5 Marks Each)
21. Find the centre of a circle passing through the points (6, -6), (3, -7) and (3, 3).
[5]
22. Show that the points (1, 7), (4, 2), (-1, -1) and (-4, 4) are the vertices of a square.
[5]
SECTION E: CASE STUDY (4 Marks)
23. Case Study: Classroom Seating
In a classroom, 4 friends are seated at points A(3, 4), B(6, 7), C(9, 4) and D(6, 1).

(i) Find the distance between A and B. (1 Mark)
(ii) Find the distance between A and C. (1 Mark)
(iii) Check if ABCD is a square. Justify your answer. (2 Marks)
[4]