Find the fourth vertex of the parallelogram whose vertices are given by (1,1),
(2, 3) and (2, -2) taken in order.

If A(1, 1), B(2, 3) and C(2, -2) are the three points of the parallelogram. Let the fourth vertex be D(x, y).
Since ABCD is a parallelogram, the midpoint of the diagonal AC = the midpoint of the diagonal BD.

We know that the midpoint of a line segment AB with A(x, y) and B(u, v) is
The midpoint of diagonal AC is

The midpoint of diagonal BD is ⇒ 3 = 2 + x and -1 = 3 + y
⇒ x = 1 and y = -4
Thus the fourth vertex is (1, -4).