Q) 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.

(Q 25A – 30/3/3 – CBSE 2026 Question Paper)

Ans:

(i) Co-ordinates of point P:

Step 1: Since the diagnols of a square bisect each other

∴ P is mid point of diagonal BD.

Step 2: Since the coordinates of mid point are given by:

∴ coordinates of P = = (5, 2)

Therefore, the co-ordinates of point P are (5, 2).

(ii) Length of the side of the square:

Step 3: Let’s first calcualte the length of the diagonal.

Since the distance between (x₁,y₁) and (x₂,y₂) is given by:

∴ Distance between (9, – 2) and (1, 6):

∴ D =

= 8√2 units

Step 4: Since in a square, Diagonal = side√2

∴ Side √2 = 8 √2

∴ Side = 8 units

Therefore, Length of the side of the square is 8 units.

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