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XAT 2015 — QA & DI Question 9

BasicsEasy

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.

Answer & solution

  • A

    15 and 30

  • B

    15 and 40

  • C

    17 and 30

  • 17 and 40

  • E

    Multiple solutions are possible

Solution

(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).

XAT 2015 QA & DI Q9: Two diagonals of a parallelogram intersect each other at coordinates (17.5, 23.5). Two adjacent points of the — Solution | TheCATExam