Two diagonals of a parallelogram intersect each other at coordinates (17.5, 23.5). Two adjacent points of the

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

17 and 40. Using distance formula, C X = ( 17.5 − 5.5 ) 2 + ( 23.5 − 7.5 ) 2 = 12 2 + 16 2 CX = \sqrt{(17.5 - 5.5)^2 + (23.5 - 7.5)^2} = \sqrt{12^2 + 16^2} C X = ( 17.5 − 5.5 ) 2 + ( 23.5 − 7.5 ) 2 ​ = 1 2 2 + 1 6 2 ​ = 144 + 256 = 400 = 20 \sqrt{144 + 256} = \sqrt{400} = 20 144 + 256 ​ = 400 ​ = 20 => A C