question_answer

Three vertices of a parallelogram taken in order are \[(-1,\,-6)\], \[(2,\,-5)\] and \[(7,\,2)\]. The fourth vertex is  [Kerala (Engg.) 2002]

A) (1, 4)

B) (4, 1)

C) (1, 1)

D) (4, 4)

Correct Answer: B

Solution :

\[\frac{-1+7}{2}=\frac{2+x}{2}\]\[\Rightarrow \,\,x=4\] \[\frac{-6+2}{2}=\frac{-5+y}{2}\]\[\Rightarrow \,\,y=1\] \[\therefore \]  Fourth vertex (x, y) is (4, 1).