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If P(1,2)Q(4,6),R(5,7), and S(a , b) are...

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=2,b=4` (b) `a=3,b=4` `a=2,b=3` (d) `a=1orb=-1`

A

`a=2,b=4`

B

`a=3,b=4`

C

`a=2,b=3`

D

`a=3,b=5`

Text Solution

Verified by Experts

`PQRS` is a parallelogram if and only if the mid point of the diagonals `PR` is same as that of the mid-point of `QS`. That is, if and only if
`(1+5)/(2)=(4+a)/(2)` and `(2+7)/(2)=(6+b)/(2)`
`impliesa=2` and `b=3`.
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