MathsCBSE Class 10 · Basic · Sample paper, session 2026-27 · 2 marks · Very short answer

CBSE Class 10 Mathematics Basic sample paper 2026-27: question 25(A)

From the official CBSE sample question paper for 2026-27, section B, question 25(A), for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q25(A) · 2 marks · Very short answerCoordinate Geometry

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 $b$ .

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

What property do the diagonals of a parallelogram have?

Hint 2

Set the midpoint of AC equal to the midpoint of BD and compare coordinates.

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.

The diagonals of a parallelogram bisect each other, so the midpoint of AC = the midpoint of BD.
½ mark
$(\frac{3 + a}{2}, \frac{1 + b}{2}) = (\frac{5 + 4}{2}, \frac{1 + 3}{2})$ , so $\frac{3 + a}{2} = \frac{9}{2}$ and $\frac{1 + b}{2} = 2$
1 mark
$a = 6, b = 3$
½ mark

Answer: $a = 6$ , $b = 3$

Where the marks are

Uses the property that the diagonals bisect each other (½ mark)
Equates the midpoints correctly (1 mark)
$a = 6$ , $b = 3$ (½ 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 (Basic): every question, by section.

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CBSE Class 10 Mathematics Basic sample paper 2026-27: question 25(A)

Hints

Step-by-step solution

Revise the chapter

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