Question

If A(- 2,1),B(a,0), C(4, b) and D(1, 2) are the vertices of a parallelogram ABCD, find the values of a and b. Hence find ihe lengths of its sides.

Answer 1

We know that diagonals of parallelogram bisect each other.

.'. Midpoint of diagonal AC

(-2+4 / 2, 1+b / 2) = (1, 1 + b / 2) Mid-point of diagonal BD

(a +1 / 2 , 0+2 / 2) = (a + 1 / 2, 1)

Mid point of diagonal AC = mid point of diagonal BD

1= a +1 / 2 and 1+b / 2 =1

:.   a=1 and b =1

ABCD is a paralielogram (Given)

AB = CD = √10 unit

BC = AD = √10 unit