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)

$a=2,b=3$

As PQRS is a parallelogram so the midpoint of PR is equal to the midpoint of QS.

$\frac{1+5}{2},\frac{7+2}{2}=\frac{a+4}{2},\frac{b+6}{2}$

$\frac{a+4}{2}=\frac{6}{2},\frac{b+6}{2}=\frac{9}{2}$

$a=2,b=3$