Quantitative Aptitude Ques 1417

Question: Three vertices of a rhombus are $ (2,-1), $ $ (3,4) $ and $ (-2,3). $ Find the fourth vertex.

Options:

A) $ (1,2) $

B) $ (3,2) $

C) $ (-2,-3) $

D) $ (-3,-2) $

E) $ (2,3) $

Show Answer

Answer:

Correct Answer: D

Solution:

  • Let coordinate of D be $ (x,y) $ and M be the intersection point of diagonals AC and BD. Since, M is the mid-point of AC.
    $ \therefore $ Coordinate of $ M=( \frac{-,2+2}{2},\frac{-1+3}{2} )=(0,1) $ Also, M is the mid-point of BD.
    $ \therefore $ Coordinate of $ M=( \frac{x+3}{2},\frac{y+4}{2} ) $
    $ \therefore $ $ \frac{x+3}{2}=0 $
    $ \Rightarrow $ $ x=-3 $ and $ \frac{y+4}{2}=1 $
    $ \Rightarrow $ $ y=-2 $
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