If `P(1,2)Q(4,6),R(5,7),` and `S(a , b)` are the vertices of a parallelogram `P Q R S ,` then (a)`a=2,b=4` (b) `a=3,b=4` (c)`a=2,b=3` (d) `a=1,b=-1`

Options

A. `a=2, b=4`
B. `a=3, b=4`
C. `a=2, b=4`
D. `a=3, b=5`

Answer

C

Explanation

Since the diagonals of a parallelogram bisect each other. Therefore, mid-points of PR and QS coincide.
`i.e.(1+5)/(2)=(4+a)/(2) and (2+7)/(2)=(6+b)/(2)rarr a=2 and b=3`