Question

Three vertices of a parallelogram ABCD are A (1, 2, 3), B (−1, −2, −1) and C (2, 3, 2). Find the coordinates of the fourth vertex D.

Answer 1

In a parallelogram, diagonals bisect each other. Therefore, if D (x, y, z) is the fourth vertex, then we have

[(1 + 2)/2, (2 + 3)/2 + (3 + 2)/2] = midpoint of AC

= Midpoint of BD 

= [(x - 1)/2, (y - 2)/2, (z - 1)/2]

Therefore 

Therefore, D = (4, 7, 6).