Question

Two diagonals of a parallelogram intersect each other at coordinates $(17.5, 23.5)$. Two adjacent points of the parallelogram are $(5.5, 7.5)$ and $(13.5, 16)$. Find the lengths of the diagonals.

Accepted Answer

D. Let intersection point be $X(17.5, 23.5)$ and vertices $C(5.5, 7.5)$ and $B(13.5, 16)$. Distance $CX = \sqrt{(17.5-5.5)^2 + (23.5-7.5)^2} = \sqrt{12^2 + 16^2} = 20$. Length of diagonal $AC = 2 	imes CX = 40$. Distance $BX = \sqrt{(17.5-13.5)^2 + (23.5-16)^2} = \sqrt{4^2 + 7.5^2} = \sqrt{16 + 56.25} = \sqrt{72.25} = 8.5$. Length of diagonal $BD = 2 	imes BX = 17$. Lengths of diagonals are 17 and 40.

Diagonals of a Parallelogram from Coordinates

Explanation

Practise this under exam conditions