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Determine the ratio in… (Class 10 Maths Basic 2023, Q29a)

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MathsCBSE Class 10 · Basic · Board exam 2023, set 430/5/1 · 3 marks · Short answer

CBSE Class 10 Mathematics Basic 2023: question 29(a)

Set in the CBSE Class 10 board exam of 2023, paper 430/5/1, section C, question 29(a), for 3 marks. Try it first; the hints and our step-by-step solution are below.

Q29(a) · 3 marks · Short answerCoordinate Geometry

Determine the ratio in which the point P(a, -2) divides the line segment joining the points A(-4, 3) and B(2, -4). Also, find the value of 'a'.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2023 board paper, set 430/5/1.

Hints

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

Hint 1

Take the ratio as k : 1 and apply the section formula.

Hint 2

The y-coordinate of P is known (−2), so use it to find k first; then find a from the x-coordinate.

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 P divide AB in ratio . By section formula, y-coordinate of P:

    1½ marks

  2. So the ratio is .

    ½ mark

  3. x-coordinate:

    1 mark

Answer: Ratio 5 : 2;

Where the marks are

  • Uses section formula on y-coordinate to get (1½ marks)
  • Ratio 5 : 2 (½ mark)
  • Finds (1 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 430/5/1 (Basic): 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.