question_answer

If P (1,2), Q(4,6) R(5, 7) and S(a, b) are the vertices of a parallelogram PQRS, then  [IIT 1998]

A) \[a=2,\,b=4\]

B) \[a=3,\,b=4\]

C) \[a=2,\,b=3\]

D) \[a=3,\,b=5\]

Correct Answer: C

Solution :

Diagonals cut each other at middle points.    Hence  \[\frac{a+4}{2}=\frac{1+5}{2}\,\,\Rightarrow \,\,a=2\]  \[\frac{b+6}{2}=\frac{2+7}{2}\,\,\Rightarrow \,\,b=3\].