Question

If the points P(a, -11), Q(5, b), R(2, 15) andS(1 ,1) are the vertices of a parallelogram PQRS, find the values of a and b.

Answer 1

The points are P (a, -11), B (5, b), C (2, 15) and D (1, 1)

Join PQ and QS, intersecting at O.

We know that the diagonals of a parallelogram bisect each other.

Therefore, O is the midpoint of PR as well as QS.

Midpoint of PQ $=(\frac{a+2}{2},\frac{-11+15}{2})=(\frac{a+2}{2},2)$

Midpoint of QS $=(\frac{5+1}{2},\frac{b+1}{2})=(3,\frac{b+1}{2})$

Therefore, $\frac{a+2}{2}=3$ and $\frac{b+1}{2}=2$

Solving we get, a = 4 and b = 3