Question 61

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.

Solution

Using distance formula,

$$CX = \sqrt{(17.5 - 5.5)^2 + (23.5 - 7.5)^2} = \sqrt{12^2 + 16^2}$$

= $$\sqrt{144 + 256} = \sqrt{400} = 20$$

=> $$AC = 2 \times CX = 40$$

$$BX = \sqrt{(17.5 - 13.5)^2 + (23.5 - 16)^2} = \sqrt{4^2 + 7.5^2}$$

= $$\sqrt{16 + 56.25} = \sqrt{72.25} = 8.5$$

=> $$BD = 2 \times BX = 17$$

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