If A (2,3), B(2,4) C(4,9) and D(x,8) are the vertices of a parallelogram ABCD, then find the value of x.

4

A(2,3), B(2,4) C(4,9) and D(x,8) are the vertices of a parallelogram ABCD.

length of parallel sides are equal

Thus, sqrt[(2-2)^2 + (4-3)^2] = sqrt[(x-4)^2 + (8-9)^2]

sqrt[1] = sqrt[(x-4)^2 + 1]

1 = (x-4)^2 + 1

(x-4)^2 = 0

The correct answer is Option (4) → 4