if A(1,2),B(4,3),C6,6) are the three vertices of a parallelogram ABCD , find the coordinates of the fourth vertex?

Let (x, y) be the coordinates of the vertex D.

 

We know that the diagonals of a parallelogram bisect each other.

 

Let us now find the midpoint of the line joining A and C.

 

Therefore, the coordinates of the midpoint of AC are 

Similarly the coordinates of the midpoint of BD are 

By the property of the parallelogram, we have

 

 

 

Thus, the coordinates of the vertex D are D=(3,5)