MathsCBSE Class 10 · Basic · Sample paper, session 2024-25 · 2 marks · Very short answer

CBSE Class 10 Mathematics Basic sample paper 2024-25: question 21(A)

From the official CBSE sample question paper for 2024-25, section B, question 21(A), for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q21(A) · 2 marks · Very short answerCoordinate Geometry

$P (x, y)$ is a point equidistant from the points $A (4, 3)$ and $B (3, 4)$ . Prove that $x - y = 0$ .

Source: official sample paper from cbseacademic.nic.in (PDF). See it in the full Sample paper 2024-25.

Hints

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

Hint 1

Equidistant means $P A = P B$ . Squaring both sides removes the square roots.

Hint 2

Expand both sides. The $x^{2}$ , $y^{2}$ and constant terms cancel.

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 $P (x, y)$ is equidistant from $A (4, 3)$ and $B (3, 4)$ , $P A = P B$ , so $P A^{2} = P B^{2}$ . By the distance formula:
$(x - 4)^{2} + (y - 3)^{2} = (x - 3)^{2} + (y - 4)^{2}$
1 mark
Expanding: $x^{2} - 8 x + 16 + y^{2} - 6 y + 9 = x^{2} - 6 x + 9 + y^{2} - 8 y + 16$ .
This gives $- 8 x - 6 y = - 6 x - 8 y$ , so $- 2 x + 2 y = 0$ .
Hence $x = y$ , i.e. $x - y = 0$ . Proved.
1 mark

Answer: $x - y = 0$ (proved)

Where the marks are

Writes $P A^{2} = P B^{2}$ using the distance formula (1 mark)
Simplifies to $x - y = 0$ (1 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 paperSample paper 2024-25 (Basic): every question, by section.

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CBSE Class 10 Mathematics Basic sample paper 2024-25: question 21(A)

Hints

Step-by-step solution

Revise the chapter

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