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

CBSE Class 10 Mathematics Standard 2025: question 26(a)

Set in the CBSE Class 10 board exam of 2025, paper 30/3/1, section C, question 26(a), for 3 marks. Try it first; the hints and our step-by-step solution are below.

Q26(a) · 3 marks · Short answerCoordinate Geometry

If the mid-point of the line segment joining the points A $(3, 4)$ and B $(k, 6)$ is P $(x, y)$ and $x + y - 10 = 0$ , find the value of k.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2025 board paper, set 30/3/1.

Hints

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

Hint 1

Use the mid-point formula to write x and y.

Hint 2

y comes out as a number, while x is in terms of k.

Hint 3

Substitute both into $x + y - 10 = 0$ and solve for k.

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.

By the mid-point formula, $x = \frac{3 + k}{2}$ .
½ mark
$y = \frac{4 + 6}{2} = 5$ .
½ mark
P lies on $x + y - 10 = 0$ , so:
$\frac{3 + k}{2} + 5 - 10 = 0$
1 mark
$\frac{3 + k}{2} = 5 \Rightarrow 3 + k = 10 \Rightarrow k = 7$ .
1 mark

Answer: k = 7

Where the marks are

Finds $x = \frac{3 + k}{2}$ (1/2 mark)
Finds $y = 5$ (1/2 mark)
Substitutes into $x + y - 10 = 0$ (1 mark)
Solves to get $k = 7$ (1 mark)

Revise the chapter

Chapter: Coordinate Geometry (notes, formulas, where marks are lost and every past question)
Topic: Midpoint Formula and Points of Trisection

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 30/3/1 (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 26(a)

Hints

Step-by-step solution

Revise the chapter

More questions from Coordinate Geometry