Question

Show that the points A(0, 1, 2), B(2, -1, 3) and C(1, -3, 1) are the vertices of an isosceles right-angled triangle.

Answer 1

Given points are the vertices of an isosceles right-angled triangle if sum of squares of two sides is equal to square of third side.

Apply distance formula:

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

Now, AB² + BC² = 9 + 9

= 18

= AC²

Therefore, Therefore, vertices A, B, C are the vertices of an isosceles right-angled triangle.