Question

Three consecutive vertices of a parallelogram are A(−6, 2, 4), B(2, 4, −8) and C(−2, 2, 4). Find the co-ordinates of the fourth vertex.

Answer 1

Let the co-ordinates of the fourth vertex be D(x, y, z) we know that the diagonals of a parallelogram bisect each other 

∴ Midpoint of AC = Midpoint of BD

⇒ x= −10 

⇒ y = 0 

⇒ z = 16

∴ Co-ordinates of D are (−10, 0, 16)