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Show that A(1, 2), B(5… (Class 10 Maths Basic 2023, Q24a)

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MathsCBSE Class 10 · Basic · Board exam 2023, set 430/5/1 · 2 marks · Very short answer

CBSE Class 10 Mathematics Basic 2023: question 24(a)

Set in the CBSE Class 10 board exam of 2023, paper 430/5/1, section B, question 24(a), for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q24(a) · 2 marks · Very short answerCoordinate Geometry

Show that A(1, 2), B(5, 4), C(3, 8) and D(-1, 6) are vertices of a parallelogram ABCD.

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

In a parallelogram, the diagonals bisect each other.

Hint 2

Find the mid-points of AC and BD using the mid-point formula and compare.

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. Mid-point of diagonal AC

    1 mark

  2. Mid-point of diagonal BD

    ½ mark

  3. The diagonals AC and BD have the same mid-point, i.e. they bisect each other. Hence ABCD is a parallelogram.

    ½ mark

Answer: Diagonals AC and BD have common mid-point (2, 5), so ABCD is a parallelogram.

Where the marks are

  • Mid-point of AC = (2, 5) (1 mark)
  • Mid-point of BD = (2, 5) (½ mark)
  • Concludes diagonals bisect each other, so parallelogram (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 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.