Let ABCD be a parallelogram in which the co-ordinates of the vertices are A (1, 2);
B (4, 3) and C (6, 6). We have to find the co-ordinates of the forth vertex.
Let the forth vertex be
Since ABCD is a parallelogram, the diagonals bisect each other. Therefore the mid-point of the diagonals of the parallelogram will coincide.
Now to find the mid-point of two pointsand we use section formula as,
The mid-point of the diagonals of the parallelogram will coincide.
Now equate the individual terms to get the unknown value. So,
So the forth vertex is