LIWA

Coordinate Geometry

CBSE Class 10 · Maths · Chapter 7

Past board exam questions

CBSE 2027 sample paper · 1 mark

The point which lies on the perpendicular bisector of the line segment joining the points A (– 3, – 4) and B (3, 4) is:

  1. (0, 0)
  2. (0, 3)
  3. (3, 0)
  4. (0, 4)
Show answer
(0, 0)

CBSE 2027 sample paper · 1 mark

If the point P (5, 2) divides the line segment joining A(8, 5) and B(4, y) in the ratio 3 : 1, then the value of y is

  1. 4
  2. 3
  3. 2
  4. 1
Show answer
1

CBSE 2027 sample paper · 1 mark

PM is a median of Δ PQR with vertices P (5, – 6), Q (6, 4) and R (0, 0). The length of PM is:

  1. 2√(17) units
  2. 2√(15) units
  3. √(101) units
  4. 10 units
Show answer
2√(17) units

CBSE 2027 sample paper · 1 mark

Assertion (A): If three vertices of a parallelogram taken in order are (–1, –6), (2, –5) and (7, 2), then its fourth vertex is (4,1). Reason (R): Diagonals of a parallelogram bisect each other.

  1. Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
  2. Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).
  3. Assertion (A) is true but Reason (R) is false.
  4. Assertion (A) is false but Reason (R) is true.
Show answer
Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).

CBSE 2027 sample paper · 2 marks

Points A (3,1), B (5, 1), C (a, b) and D (4, 3) are vertices of a parallelogram ABCD. Find the values of a and b.

Show answer
The diagonals of a parallelogram bisect each other, so mid-point of AC = mid-point of BD. ((3 + a)/(2), (1 + b)/(2)) = ((5 + 4)/(2), (1 + 3)/(2)) (3 + a)/(2) = (9)/(2) ⇒ a = 6 and (1 + b)/(2) = 2 ⇒ b = 3.

CBSE 2027 sample paper · 3 marks

Determine the ratio in which the point (– 6, y) divides the line segment joining the points A (–3, –1) and B (– 8, 9). Also, find the value of y.

Show answer
Let the point divide AB in the ratio k : 1. Its coordinates are ((-8k - 3)/(k + 1), (9k - 1)/(k + 1)). (-8k - 3)/(k + 1) = -6 ⇒ -8k - 3 = -6k - 6 ⇒ k = (3)/(2), i.e. the required ratio is 3 : 2. y = (9((3)/(2)) - 1)/((3)/(2) + 1) = ((25)/(2))/((5)/(2)) = 5.

CBSE 2027 sample paper · 2 marks

Find a linear relation between x and y such that P (x, y) is equidistant from the points A (1, 4) and B (–1, 2).

Show answer
PA = PB ⇒ √((x - 1)2 + (y - 4)2) = √((x + 1)2 + (y - 2)2) ⇒ x2 - 2x + 1 + y2 - 8y + 16 = x2 + 2x + 1 + y2 - 4y + 4 ⇒ 4x + 4y = 12 ⇒ x + y = 3.

CBSE 2026 board paper · 1 mark

5 trees Banyan, Silver Oak, Orange, Amla and Mango were planted in the garden at the points Banyan (–3, 4), Silver Oak (3, 4), Orange (0, 7), Amla (–2, 0) and Mango (2, 0). If 1 unit = 1 m, which of the following trees are at a distance of 4 metres ?

  1. Amla and Mango
  2. Mango and Silver Oak
  3. Silver Oak and Orange
  4. Orange and Mango
Show answer
Amla and Mango