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.
Explanation:
(13.5, 16) and (5.5, 7.5) are adjacent points of the parallelogram and (17.5, 23.5) is the point of intersection of two diagonals of the parallelogram.
Property: Diagonals of a parallelogram bisect each other.
Distance between (17.5, 23.5) and (5.5, 7.5):
(17.5-5.5)2+(23.5-7.5)2=20
Length of diagonal that passes through (17.5, 23.5) and (5.5, 7.5) = 20 × 2 = 40 cm Distance between (17.5, 23.5) and (13.5, 16):
(17.5-13.5)2+(23.5-16)2=8.5
Length of diagonal that passes through (17.5, 23.5) and (13.5, 16) = 8.5 × 2 = 17 cm
Hence, option (d).
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