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

Question

Philoid · Accepted Answer

We know that the diagonals of a parallelogram bisect each other

So the coordinates of the mid – point of the PR = Coordinates of the mid – point of the QS

{(2 + a)/2,(15 – 11)/2} = {(5 + 1)/2,(b + 1)/2}

2 + a = 6

a = 4

15 – 11 = b + 1

4 = b + 1

b = 3

Hence, a = 4, b = 3