Three vertices of a parallelogram ABCD are A (3, 1, 2), B (1, 2, 4) andC ( 1, - Maths - Introduction to Three Dimensional Geometry

Question

Three vertices of a parallelogram ABCD are A (3, –1, 2), B
(1, 2, –4) andC (–1, 1, 2) Find the coordinates of the
fourth vertex

Gopal Mohanty · Accepted Answer

The three vertices of a parallelogram ABCD are given as A (3, –1, 2), B (1, 2, –4), and C (–1, 1, 2) Let the coordinates of the fourth vertex be D (x, y, z)

We know that the diagonals of a parallelogram bisect each other Therefore, in parallelogram ABCD, AC and BD bisect each other ∴Mid-point of AC = Mid-point of BD

⇒ x = 1, y = –2, and z = 8 Thus, the coordinates of the fourth vertex are (1, –2, 8)

Three vertices of a parallelogram ABCD are A (3, –1, 2), B (1, 2, –4) andC (–1, 1, 2). Find the coordinates of the fourth vertex.