# Three vertices of a parallelogram are (a + b, a — b), (2a + b, 2a — b), (a — b, a + b). Find the fourth vertex.

7.4k views

Three vertices of a parallelogram are (a + b, a - b), (2a + b, 2a - b), (a - b, a + b). Find the fourth vertex.

by (13.2k points)
selected

Let A(a + b, a - b), B(2a + b, 2a - b), C(a - b, a + b) and (x,y) be the given points

Since, the diagonals of a parallelogram bisect each other

Therefore, Coordinates of the midpoint of AC =Coordinates of the midpoint of BD

Hence, the fourth vertex is (-b,b)