MathsCBSE Class 10 · Standard · Board exam 2025, set 30/6/1 · 2 marks · Very short answer

CBSE Class 10 Mathematics Standard 2025: question 23

Set in the CBSE Class 10 board exam of 2025, paper 30/6/1, section B, question 23, for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q23 · 2 marks · Very short answerCoordinate Geometry

Prove that abscissa of a point P which is equidistant from points with coordinates A(7, 1) and B(3, 5) is 2 more than its ordinate.

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

Take P as $(x, y)$ and equate its distances from A and B.

Hint 2

Square both distances; the $x^{2}$ and $y^{2}$ terms cancel, leaving a linear relation.

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.

Let $P (x, y)$ be equidistant from A(7, 1) and B(3, 5). Then $P A = P B \Rightarrow P A^{2} = P B^{2}$ .
½ mark
$(x - 7)^{2} + (y - 1)^{2} = (x - 3)^{2} + (y - 5)^{2}$ [distance formula]
½ mark
$x^{2} - 14 x + 49 + y^{2} - 2 y + 1 = x^{2} - 6 x + 9 + y^{2} - 10 y + 25 \Rightarrow - 8 x + 8 y + 16 = 0$
½ mark
$\Rightarrow x = y + 2$ . So the abscissa of P is 2 more than its ordinate. Hence proved.
½ mark

Answer: $x = y + 2$ (proved)

Where the marks are

Writes $P A^{2} = P B^{2}$ (½ mark)
Applies distance formula correctly (½ mark)
Expands and simplifies (½ mark)
Concludes $x = y + 2$ (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 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 23

Hints

Step-by-step solution

Revise the chapter

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