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

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 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)

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