Diagonals AC and BD of square ABCD intersect at P. Coordinates of points B and D are (9, -2) and (1, 6) respectively. (i) Find the co-ordinates of point P. (ii) Find the length of the side of the square.

MathsCBSE Class 10 · Standard · Board exam 2026, set 30/3/1 · 2 marks · Very short answer

CBSE Class 10 Mathematics Standard 2026: question 23(a)

Set in the CBSE Class 10 board exam of 2026, paper 30/3/1, section B, question 23(a), for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q23(a) · 2 marks · Very short answerCoordinate Geometry

Diagonals AC and BD of square ABCD intersect at P. Coordinates of points B and D are (9, -2) and (1, 6) respectively.

(i)
Find the co-ordinates of point P.
1 mark
(ii)
Find the length of the side of the square.
1 mark

Figure in the paper: Square ABCD with A at bottom-left, B at bottom-right (9, -2), C at top-right, D at top-left (1, 6). Diagonals AC and BD cross at P. See it in the official paper.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2026 board paper, set 30/3/1.

Hints

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

Hint 1

The diagonals of a square bisect each other. Where does that put P on BD?

Hint 2

Find BD by the distance formula, then use diagonal = side × √2.

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.

(i) The diagonals of a square bisect each other, so P is the midpoint of BD: $P = (\frac{9 + 1}{2}, \frac{- 2 + 6}{2}) = (5, 2)$ .
1 mark
(ii) $B D = (9 - 1)^{2} + (- 2 - 6)^{2} = 64 + 64 = 128 = 82$ . In a square, diagonal $= 2 \times$ side, so $2 A B^{2} = B D^{2} = 128$ .
½ mark
(ii) $A B^{2} = 64 \Rightarrow A B = 8$ . The side of the square is 8 units.
½ mark

Answer: (i) P(5, 2); (ii) 8 units

Where the marks are

(i) Uses the midpoint formula to get P(5, 2) (1 mark)
(ii) Uses $2 A B^{2} = B D^{2}$ with $B D^{2} = 128$ (½ mark)
(ii) Gets side = 8 units (½ mark)

Revise the chapter

Chapter: Coordinate Geometry (notes, formulas, where marks are lost and every past question)
Topic: Distance Formula

Practise this chapterBoard-style questions from Coordinate Geometry, one at a time, marked against the answer key and marking points.Back to the full paper2026 board paper, set 30/3/1 (Standard): every question, by section.

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CBSE Class 10 Mathematics Standard 2026: question 23(a)

Hints

Step-by-step solution

Revise the chapter

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