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Find the ratio in which y-axis… (Class 10 Maths 2023, Q24)

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

CBSE Class 10 Mathematics Standard 2023: question 24

Set in the CBSE Class 10 board exam of 2023, paper 30/5/1, section B, question 24, for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q24 · 2 marks · Very short answerCoordinate Geometry

Find the ratio in which y-axis divides the line segment joining the points and .

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

What is the x-coordinate of any point on the y-axis?

Hint 2

Take the ratio as k : 1 and write only the x-coordinate using the section formula, then set it equal to 0.

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 the y-axis divide the segment joining A(5, −6) and B(−1, −4) in the ratio at the point P. Every point on the y-axis has x-coordinate 0, so P = .

    ½ mark

  2. By the section formula, x-coordinate of P: .

    1 mark

  3. Hence the y-axis divides the segment in the ratio (internally).

    ½ mark

Answer: 5 : 1

Where the marks are

  • Takes ratio k : 1 and point of division (0, y) on the y-axis (½ mark)
  • Equates the x-coordinate from the section formula to 0 and gets k = 5 (1 mark)
  • States the ratio 5 : 1 (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 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.