MathsCBSE Class 10 · Basic · Board exam 2025, set 430/4/1 · 3 marks · Short answer

CBSE Class 10 Mathematics Basic 2025: question 29(a)

Set in the CBSE Class 10 board exam of 2025, paper 430/4/1, section C, question 29(a), for 3 marks. Try it first; the hints and our step-by-step solution are below.

Q29(a) · 3 marks · Short answerCoordinate Geometry

If points A $(- 5, y)$ , B $(2, - 2)$ , C $(8, 4)$ and D $(x, 5)$ taken in order, form a parallelogram ABCD, then find the values of $x$ and $y$ . Hence, find lengths of sides of the parallelogram.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2025 board paper, set 430/4/1.

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

Equate the mid-point of AC with the mid-point of BD to get $x$ and $y$ .

Hint 3

Use the distance formula for AB and BC; the opposite sides are equal.

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 mid-point of BD = the mid-point of AC: $(\frac{2 + x}{2}, \frac{- 2 + 5}{2}) = (\frac{- 5 + 8}{2}, \frac{y + 4}{2})$
1 mark
$\frac{2 + x}{2} = \frac{3}{2} \Rightarrow x = 1$ ; $\frac{3}{2} = \frac{y + 4}{2} \Rightarrow y = - 1$
1 mark
So A $(- 5, - 1)$ , B $(2, - 2)$ , C $(8, 4)$ , D $(1, 5)$ . $A B = (2 + 5)^{2} + (- 2 + 1)^{2} = 49 + 1 = 50 = 52$ units $= C D$
½ mark
$B C = (8 - 2)^{2} + (4 + 2)^{2} = 36 + 36 = 72 = 62$ units $= A D$
½ mark

Answer: $x = 1$ , $y = - 1$ ; sides AB = CD = $52$ units, BC = AD = $62$ units

Where the marks are

Equates the mid-points of the diagonals AC and BD (1 mark)
Gets $x = 1$ and $y = - 1$ (½ + ½ marks)
$A B = 52$ (½ mark)
$B C = 62$ (½ mark)

Revise the chapter

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

Practise this chapterBoard-style questions from Coordinate Geometry, one at a time, marked against the answer key and marking points.Back to the full paper2025 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 2025: question 29(a)

Hints

Step-by-step solution

Revise the chapter

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