Question

The three vertices of a parallelogram are (3, 4) (3, 8) and (9, 8). Find the fourth vertex.

Answer 1

We are given three vertices of a parallelogram A(3, 4), B(3, 8) and C(9, 8).

We know that diagonals of a parallelogram bisect each other. Let the fourth vertex be D(x, y).
Mid point of BD = $\left(\frac{x+3}{2},\frac{y+8}{2}\right)$
Mid point of AC = $\left(\frac{9+3}{2},\frac{4+8}{2}\right)$ = $\left(6,6\right)$
Since the mid point of BD = mid point of AC
So, $\left(\frac{x+3}{2},\frac{y+8}{2}\right)$ = (6, 6)
Thus, x = 9, y = 4.
So, the fourth vertex is (9, 4).