Quantitative Aptitude Ques 2047

Question: If two vertices of a triangle are (5, 4) and $ (-2,4) $ and centroid is (5, 6), then third vertex is

Options:

A) $ (12,10) $

B) $ (12,10) $

C) $ (-10,12) $

D) $ (12,-10) $

E) $ (-10,-12) $

Show Answer

Answer:

Correct Answer: A

Solution:

  • Let third vertex be $ (x,y). $ Coordinate of centroid $ =( \frac{x _1+x _2+x _3}{3},\frac{y _1+y _2+y _3}{3} ) $ Given, $ x _1=x, $ $ x _2=5, $ $ x _3=-2 $ $ y _1=y, $ $ y _2=4, $ $ y _3=4 $ and centroid $ =(5,6) $

$ \Rightarrow $ $ 5=\frac{x+5-2}{3} $
$ \Rightarrow $ $ x=12 $

$ \Rightarrow $ $ 6=\frac{y+4+4}{3} $
$ \Rightarrow $ $ y=10 $

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