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A line intersects y-axis and… (Class 10 Maths 2023, Q22)

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MathsCBSE Class 10 · Standard · Board exam 2023, set 30/6/1 · 2 marks · Very short answer

CBSE Class 10 Mathematics Standard 2023: question 22

Set in the CBSE Class 10 board exam of 2023, paper 30/6/1, section B, question 22, for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q22 · 2 marks · Very short answerCoordinate Geometry

A line intersects y-axis and x-axis at point P and Q, respectively. If R(2, 5) is the mid-point of line segment PQ, then find the coordinates of P and Q.

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

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

Hint 2

Use the mid-point formula with R(2, 5).

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. P lies on the y-axis and Q lies on the x-axis, so let and .

    ½ mark

  2. R(2, 5) is the mid-point of PQ, so by the mid-point formula .

    ½ mark

  3. Similarly .

    ½ mark

  4. Hence and .

    ½ mark

Answer: P(0, 10), Q(4, 0)

Where the marks are

  • Takes P(0, y) and Q(x, 0) (½ mark)
  • Applies the mid-point formula to get x = 4 (½ mark)
  • Gets y = 10 (½ mark)
  • States P(0, 10) and Q(4, 0) (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.