MathsCBSE Class 10 · Standard · Board exam 2023, set 30/5/1 · 2 marks · Very short answer

CBSE Class 10 Mathematics Standard 2023: question 21(b)

Set in the CBSE Class 10 board exam of 2023, paper 30/5/1, section B, question 21(b), for 2 marks. Try it first; the hints and our step-by-step solution are below.

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

Point P(x, y) is equidistant from points A(5, 1) and B(1, 5). Prove that $x = y$ .

Source: official question paper from cbse.gov.in (PDF). See it in the full 2023 board paper, set 30/5/1.

Hints

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

Hint 1

'Equidistant' means PA = PB.

Hint 2

Square both distances to avoid square roots, then expand and cancel the $x^{2}$ and $y^{2}$ terms.

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.

P is equidistant from A and B, so $P A = P B$ , i.e. $P A^{2} = P B^{2}$ . By the distance formula:
$(x - 5)^{2} + (y - 1)^{2} = (x - 1)^{2} + (y - 5)^{2}$ .
1 mark
Expanding: $x^{2} - 10 x + 25 + y^{2} - 2 y + 1 = x^{2} - 2 x + 1 + y^{2} - 10 y + 25$
$\Rightarrow - 10 x - 2 y = - 2 x - 10 y \Rightarrow - 8 x = - 8 y \Rightarrow x = y$ . Hence proved.
1 mark

Answer: PA² = PB² simplifies to x = y (proved).

Where the marks are

Writes PA² = PB² using the distance formula (1 mark)
Simplifies correctly to x = y (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 paper2023 board paper, set 30/5/1 (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 2023: question 21(b)

Hints

Step-by-step solution

Revise the chapter

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