MathsCBSE Class 10 · Standard · Board exam 2025, set 30/6/1 · 3 marks · Short answer

CBSE Class 10 Mathematics Standard 2025: question 29

Set in the CBSE Class 10 board exam of 2025, paper 30/6/1, section C, question 29, for 3 marks. Try it first; the hints and our step-by-step solution are below.

Q29 · 3 marks · Short answerCoordinate Geometry

If the points A(6, 1), B(p, 2), C(9, 4) and D(7, q) are the vertices of a parallelogram ABCD, then find the values of p and q. Hence, check whether ABCD is a rectangle or not.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2025 board paper, set 30/6/1.

Hints

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

Hint 1

Diagonals of a parallelogram bisect each other.

Hint 2

A parallelogram is a rectangle only if its diagonals are equal — compare 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.

Diagonals of a parallelogram bisect each other, so midpoint of AC = midpoint of BD: $(\frac{6 + 9}{2}, \frac{1 + 4}{2}) = (\frac{p + 7}{2}, \frac{2 + q}{2})$
1 mark
$p + 7 = 15 \Rightarrow p = 8$ ; $2 + q = 5 \Rightarrow q = 3$
½ mark
$A C = (9 - 6)^{2} + (4 - 1)^{2} = 18 = 32$
½ mark
With B(8, 2), D(7, 3): $B D = (7 - 8)^{2} + (3 - 2)^{2} = 2$
½ mark
Since $A C \neq = B D$ (diagonals unequal), ABCD is not a rectangle.
½ mark

Answer: $p = 8$ , $q = 3$ ; ABCD is not a rectangle

Where the marks are

Equates midpoints of diagonals (1 mark)
Finds $p = 8$ , $q = 3$ (½ mark)
$A C = 32$ (½ mark)
$B D = 2$ (½ mark)
Concludes not a rectangle (½ mark)

Revise the chapter

Chapter: Coordinate Geometry (notes, formulas, where marks are lost and every past question)
Topic: Finding the Ratio and Unknowns with Section 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 30/6/1 (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 2025: question 29

Hints

Step-by-step solution

Revise the chapter

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