Question

If the points A(a, –11), B(5, b), C(2, 15) and D(1, 1) are the vertices of a parallelogram ABCD, find the values of a and b.

Answer 1

ABCD is a parallelogram, if the mid-points of diagonals AC and BD have the same co-ordinates 

(∵ Diagonals of a parallelogram bisect each other)

Co-ordinates of mid-point of AC are \(\bigg(\frac{a+2}{2},\frac{-11+15}{2}\bigg)\) = \(\bigg(\frac{a+2}{2},2\bigg)\)

Co-ordinates of mid-point of BD are \(\bigg(\frac{5+1}{2},\frac{b+1}{2}\bigg)\) = \(\bigg(3,\frac{a+2}{2}\bigg)\)

Here, \(\frac{a+2}{2}\) = 3 and 2 = \(\frac{b+1}{2}\) ⇒ a = 4, b = 3.