Question

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

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

Answer 1

Answer: (C)

a = 2, b = 3

Answer 2

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
$\frac{1+5}{2}=\frac{4+a}{2} and \frac{2+7}{2}=\frac{6+b}{2}$
$\Rightarrow a = 2 and 6=3.$