MathsCBSE Class 10 · Standard · Sample paper, session 2026-27 · 1 mark · Assertion-reason

CBSE Class 10 Mathematics Standard sample paper 2026-27: question 19

From the official CBSE sample question paper for 2026-27, section A, question 19, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q19 · 1 mark · Assertion-reasonCompetency-basedCoordinate Geometry

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.
Options: (A) Both A and R are true and R is the correct explanation of A. (B) Both A and R are true but R is not the correct explanation of A. (C) A is true but R is false. (D) A is false but R is true.

(A)Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
(B)Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).
(C)Assertion (A) is true but Reason (R) is false.
(D)Assertion (A) is false but Reason (R) is true.

Source: official sample paper from cbseacademic.nic.in (PDF). See it in the full Sample paper 2026-27.

Hints

Open one hint at a time and try again before the next.

Hint 1

The diagonals of a parallelogram have the same mid-point.

Hint 2

Equate the mid-points of AC and BD.

Step-by-step solution

Each step shows the marks it earns, as an examiner would award them. Checked by an independent re-solve from the question paper.

Let the vertices be $A (- 1, - 6)$ , $B (2, - 5)$ , $C (7, 2)$ , $D (x, y)$ . Diagonals AC and BD bisect each other, so they share a mid-point. Mid-point of AC $= (3, - 2)$ .
$\frac{2 + x}{2} = 3 \Rightarrow x = 4$ and $\frac{- 5 + y}{2} = - 2 \Rightarrow y = 1$ . So $D = (4, 1)$ and A is true.
R is a true property, and it is exactly what was used to find D. So R correctly explains A: option (A).
1 mark

Answer: Option (A)

Where the marks are

Uses mid-points of the diagonals to get (4, 1) and recognises R as the explanation (1 mark)

Revise the chapter

Chapter: Coordinate Geometry (notes, formulas, where marks are lost and every past question)

Practise this chapterBoard-style questions from Coordinate Geometry, one at a time, marked against the answer key and marking points.Back to the full paperSample paper 2026-27 (Standard): every question, by section.

The question is transcribed from the official paper; figures are described in words. The solution, hints and chapter tag are ours. Spotted an error? Write tosupport@questionbuddy.in.

CBSE Class 10 Mathematics Standard sample paper 2026-27: question 19

Hints

Step-by-step solution

Revise the chapter

More questions from Coordinate Geometry