Question

If the points A (a, –10), B (6, b), C (3, 16), D (2, –1) are the vertices of a parallelogram ABCD, find the values of a and b.

Answer 1

Since the diagonals of a parallelogram bisect each other, the co-ordinates of the mid-points of the diagonals AC and BD of parallelogram ABCD will be equal. Now, 

Co-ordinates of mid-point of AC are \(\bigg(\frac{a+3}{2},\frac{-10+16}{2}\bigg),i.e,\,\) \(\bigg(\frac{a+3}{2},3\bigg)\)

Co-ordinates of mid-point of BD are \(\bigg(\frac{6+2}{2},\frac{b-1}{2}\bigg),i.e,\,\) \(\bigg(4,\frac{b-1}{2}\bigg)\)

⇒ \(\frac{a+3}{2}\) = 4 and 3 = \(\frac{b-1}{2}\) ⇒ a + 3 = 8 and b – 1 = 6

⇒ a = 5 and b = 7.