Question

Show that the points A(1, -1, -5), B(3, 1,3) and C(9, 1, -3) are the vertices of an equilateral triangle.

Answer 1

Given points are the vertices of an equilateral triangle if measure of all the sides are equal.

Apply distance formula:

The distance between two points (x₁,y₁,z₁) and (x₂,y₂,z₂) is given by

Length AB:

Length BC:

=> AB = BC = AC

Therefore, Points A, B, C are vertices of an equilateral triangle.