MathsCBSE Class 10 · Standard · Board exam 2025, set 30/4/1 · 3 marks · Short answer

CBSE Class 10 Mathematics Standard 2025: question 28

Set in the CBSE Class 10 board exam of 2025, paper 30/4/1, section C, question 28, for 3 marks. Try it first; the hints and our step-by-step solution are below.

Q28 · 3 marks · Short answerCoordinate Geometry

P $(x, y)$ , Q $(- 2, - 3)$ and R $(2, 3)$ are the vertices of a right triangle PQR right angled at P. Find the relationship between $x$ and $y$ . Hence, find all possible values of $x$ for which $y = 2$ .

Source: official question paper from cbse.gov.in (PDF). See it in the full 2025 board paper, set 30/4/1.

Hints

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

Hint 1

The hypotenuse is QR since the right angle is at P.

Hint 2

Write $P Q^{2} + P R^{2} = Q R^{2}$ using the distance formula and simplify.

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.

Since $∠ P = 9 0^{\circ}$ , by Pythagoras theorem $P Q^{2} + P R^{2} = Q R^{2}$ :
$(x + 2)^{2} + (y + 3)^{2} + (x - 2)^{2} + (y - 3)^{2} = 4^{2} + 6^{2} = 52$
1 mark
$2 x^{2} + 2 y^{2} + 26 = 52 \Rightarrow x^{2} + y^{2} = 13$ (required relation)
1 mark
For $y = 2$ : $x^{2} = 13 - 4 = 9 \Rightarrow x = \pm 3$
1 mark

Answer: $x^{2} + y^{2} = 13$ ; $x = 3$ or $x = - 3$

Where the marks are

Applies Pythagoras with distance formula (1 mark)
Simplifies to $x^{2} + y^{2} = 13$ (1 mark)
Finds $x = \pm 3$ (1 mark)

Revise the chapter

Chapter: Coordinate Geometry (notes, formulas, where marks are lost and every past question)
Topic: Applications of the 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 30/4/1 (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 28

Hints

Step-by-step solution

Revise the chapter

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