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Find the ratio in which the… (Class 10 Maths 2023, Q26)

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MathsCBSE Class 10 · Standard · Board exam 2023, set 30/6/1 · 3 marks · Short answer

CBSE Class 10 Mathematics Standard 2023: question 26

Set in the CBSE Class 10 board exam of 2023, paper 30/6/1, section C, question 26, for 3 marks. Try it first; the hints and our step-by-step solution are below.

Q26 · 3 marks · Short answerCoordinate Geometry

Find the ratio in which the line segment joining the points A(6, 3) and B(-2, -5) is divided by x-axis.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2023 board paper, set 30/6/1.

Hints

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

Hint 1

Any point on the x-axis has y-coordinate 0.

Hint 2

Use the section formula only for the y-coordinate and 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 x-axis cut AB at , dividing AB in the ratio .

    ½ mark

  2. By the section formula, the y-coordinate of P is . Since P lies on the x-axis, .

    2 marks

  3. Hence the required ratio is (internally).

    ½ mark

Answer: 3 : 5

Where the marks are

  • Takes the point (x, 0) dividing AB in k : 1 (½ mark)
  • Uses the section formula for the y-coordinate and gets k = 3/5 (2 marks)
  • States the ratio 3 : 5 (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 30/6/1 (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.