Q29 of 180 Page 2

Calculate the fourth vertex D of a parallelogram ABCD whose three vertices are A(– 2, 3), B(6, 7) and C(8, 3).

Given a parallelogram ABCD whose three vertices are


A (– 2, 3), B (6, 7) and C (8, 3)



Let the fourth vertex of parallelogram, D = (x, y) and L, M be the mid points of AC and BD, respectively.


We know that diagonals of a parallelogram bisects each other.


Therefore, mid – point of AC = mid – point of BD


Coordinate of L = Coordinate of M




Equating the coordinates of both sides.


3 = and 3 =


⇒ 6 + x = 6 and 7 + y = 6


⇒ x = 0 and y = – 1


Hence, the fourth vertex of parallelogram is D = (0, – 1)


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