MathsCBSE Class 10 · Standard · Board exam 2024, set 30/1/1 · 3 marks · Short answer

CBSE Class 10 Mathematics Standard 2024: question 26(B)

Set in the CBSE Class 10 board exam of 2024, paper 30/1/1, section C, question 26(B), for 3 marks. Try it first; the hints and our step-by-step solution are below.

Q26(B) · 3 marks · Short answerCoordinate Geometry

ABCD is a rectangle formed by the points A (-1, -1), B (-1, 6), C (3, 6) and D (3, -1). P, Q, R and S are mid-points of sides AB, BC, CD and DA respectively. Show that diagonals of the quadrilateral PQRS bisect each other.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2024 board paper, set 30/1/1.

Hints

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

Hint 1

First find P, Q, R, S using the mid-point formula.

Hint 2

Diagonals bisect each other exactly when they share the same mid-point.

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.

Use the mid-point formula $(\frac{x _{1} + x _{2}}{2}, \frac{y _{1} + y _{2}}{2})$ .
P, the mid-point of AB: $(\frac{- 1 - 1}{2}, \frac{- 1 + 6}{2}) = (- 1, \frac{5}{2})$ .
½ mark
Q, the mid-point of BC: $(\frac{- 1 + 3}{2}, \frac{6 + 6}{2}) = (1, 6)$ .
½ mark
R, the mid-point of CD: $(\frac{3 + 3}{2}, \frac{6 - 1}{2}) = (3, \frac{5}{2})$ .
½ mark
S, the mid-point of DA: $(\frac{3 - 1}{2}, \frac{- 1 - 1}{2}) = (1, - 1)$ .
½ mark
Mid-point of diagonal PR: $(\frac{- 1 + 3}{2}, \frac{\frac{5}{2} + \frac{5}{2}}{2}) = (1, \frac{5}{2})$ .
½ mark
Mid-point of diagonal QS: $(\frac{1 + 1}{2}, \frac{6 - 1}{2}) = (1, \frac{5}{2})$ .
Both diagonals have the same mid-point, so the diagonals PR and QS of PQRS bisect each other.
½ mark

Answer: P(−1, 5/2), Q(1, 6), R(3, 5/2), S(1, −1). Both diagonals PR and QS have mid-point (1, 5/2), so they bisect each other.

Where the marks are

Coordinates of P (½ mark)
Coordinates of Q (½ mark)
Coordinates of R (½ mark)
Coordinates of S (½ mark)
Mid-point of PR is (1, 5/2) (½ mark)
Mid-point of QS is (1, 5/2), with the conclusion (½ mark)

Revise the chapter

Chapter: Coordinate Geometry (notes, formulas, where marks are lost and every past question)
Topic: Midpoint Formula and Points of Trisection

Practise this chapterBoard-style questions from Coordinate Geometry, one at a time, marked against the answer key and marking points.Back to the full paper2024 board paper, set 30/1/1 (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.

CBSE Class 10 Mathematics Standard 2024: question 26(B)

Hints

Step-by-step solution

Revise the chapter

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