To determine if triangle ABC is isosceles, the lengths of its sides AB, BC, and AC must be calculated using the distance formula. The distances are found to be AB = √((7 - (-1))² + ((-2) - (-8))²), BC = √((-1 - 5)² + ((-8) - 0)²), and AC = √((7 - 5)² + ((-2) - 0)²). After calculating, if any two sides are equal, the triangle is classified as isosceles. The discussion focuses on verifying the equality of these side lengths. The conclusion will confirm whether triangle ABC is isosceles based on the calculated distances.