Quantitative Aptitude Ques 1196

Question: If the point A (6, 1), B (8, 2), C (9, 4) and D (p, 3) are the vertices of a parallelogram taken in order, find the value of p.

Options:

A) 3

B) 4

C) 5

D) 6

E) 7

Show Answer

Answer:

Correct Answer: E

Solution:

  • Diagonal of a parallelogram bisect each other. So, the coordinate of mid-point of AC = coordinate or mid-point of BD

$ \Rightarrow $ $ ( \frac{6+9}{2},\frac{1+4}{2} )=( \frac{8+P}{2},\frac{2+3}{2} ) $ $ ( \frac{15}{2},\frac{5}{2} )=( \frac{8+P}{2},\frac{5}{2} ) $ On comparing, $ \frac{8+P}{2}=\frac{15}{2} $

$ \Rightarrow $ $ 16+2p=30 $

$ \Rightarrow $ $ 2p=30-16 $

$ \Rightarrow $ $ 2P=14 $
$ \Rightarrow $ $ P=7 $

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