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P(–2, 5) and Q(3, 2) are two… (Class 10 Maths 2024, Q29b)

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MathsCBSE Class 10 · Standard · Board exam 2024, set 30/3/1 · 3 marks · Short answer

CBSE Class 10 Mathematics Standard 2024: question 29(b)

Set in the CBSE Class 10 board exam of 2024, paper 30/3/1, section C, question 29(b), for 3 marks. Try it first; the hints and our step-by-step solution are below.

Q29(b) · 3 marks · Short answerCoordinate Geometry

P(–2, 5) and Q(3, 2) are two points. Find the coordinates of the point R on line segment PQ such that PR = 2QR.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2024 board paper, set 30/3/1.

Hints

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

Hint 1

Turn into a ratio .

Hint 2

Use the section formula with ratio 2 : 1, where the ratio 2 goes with Q's coordinates.

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.

  1. Let lie on PQ. Since , .

    ½ mark

  2. By the section formula with , , P(–2, 5) and Q(3, 2): .

    1 mark

  3. .

    1 mark

  4. Hence the coordinates of R are .

    ½ mark

Answer: R(4/3, 3)

Where the marks are

  • Writes (½ mark)
  • Correct x-coordinate by the section formula (1 mark)
  • Correct y-coordinate 3 (1 mark)
  • States R as (½ mark)

Revise the chapter

Practise this chapterBoard-style questions from Coordinate Geometry, one at a time, marked against the answer key and marking points.Back to the full paper2024 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.