Question

Find the lengths of the sides of the triangle with the indicated vertices, and determine whether the triangle is a right triangle, an isosceles triangle, or neither. A(−1, 0, −2), b(−1, 5, 2), c(−3, −1, 1)

Answer 1

Differences AB, BC, and CA are {0, -5, -4}, {2, 6, 1}, {-2, -1, 3}, respectively. The lengths associated with these differences are

... √(0² +(-5)² +(-4)²) = √41

... √(2² +6² +1²) = √41

... √((-2)² +(-1)² +3²) = √14

Two of the legs of the triangle are the same length (√41), so the triangle is isosceles.