Given points A (-1.5.3) B (7, -1.3) B (7, -1.3) C (3, -2.6) prove that triangle ABC is rectangular

Points are given: A (-1; 5; 3), B (7; -1; 3), C (3; -2; 6).

Let us prove that triangle ABC is right-angled.

Let’s find the lengths of the sides of the triangle.

| AB | = ((7 + 1) ^ 2 + (-1 -5) ^ 2 + (3 – 3) ^ 2)) ^ (1/2) = (64 + 36) ^ (1/2) = 10;

| BC | = ((3 – 7) ^ 2 + (-2 + 1) ^ 2 + (6 – 3) ^ 2)) ^ (1/2) = (16 + 1 + 9) ^ (1/2) = 26 ^ (1/2).

| AC | = ((3 + 1) ^ 2 + (-2 – 5) ^ 2 + (6 – 3) ^ 2) ^ (1/2) = (16 + 49 + 9) ^ (1/2) = 74 ^ (1/2).

Let’s check the Pythagorean theorem in a triangle:

10 ^ 2 = (26 ^ (1/2)) ^ 2 + (74 ^ (1/2)) ^ 2;

100 = 26 + 74.

The theorem is correct – the triangle is rectangular.