MathsCBSE Class 10 · Basic · Board exam 2026, set 430/4/1 · 3 marks · Short answer

CBSE Class 10 Mathematics Basic 2026: question 31(a)

Set in the CBSE Class 10 board exam of 2026, paper 430/4/1, section C, question 31(a), for 3 marks. Try it first; the hints and our step-by-step solution are below.

Q31(a) · 3 marks · Short answerCoordinate Geometry

The vertices of a rhombus ABCD are $A (-3, -4)$ , $B (5, -3)$ , $C (1, 4)$ and $D (-7, 3)$ . Find the length of both the diagonals. Hence, find area of the rhombus ABCD.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2026 board paper, set 430/4/1.

Hints

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

Hint 1

The diagonals of rhombus ABCD are AC and BD.

Hint 2

Use the distance formula for each diagonal.

Hint 3

Area of a rhombus is half the product of its diagonals.

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.

$A C = (1 + 3)^{2} + (4 + 4)^{2} = 16 + 64 = 80 = 45$ units
1 mark
$B D = (- 7 - 5)^{2} + (3 + 3)^{2} = 144 + 36 = 180 = 65$ units
1 mark
Area of rhombus $= \frac{1}{2} \times d_{1} \times d_{2} = \frac{1}{2} \times 45 \times 65 = \frac{1}{2} \times 120 = 60$ square units
1 mark

Answer: AC = $45$ units, BD = $65$ units, Area = 60 sq. units

Where the marks are

$A C = 45$ (1 mark)
$B D = 65$ (1 mark)
Area $= \frac{1}{2} d_{1} d_{2} = 60$ sq units (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 paper2026 board paper, set 430/4/1 (Basic): 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 Basic 2026: question 31(a)

Hints

Step-by-step solution

Revise the chapter

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