Question

Explain how you know that RST is a right triangle.

Answer 1

See below ~

Explanation:

Finding the lengths of the sides :

• a = √(5 - 1)² + (-5 + 5)² = √(4)² = 4
• b = √(1 - 1)² + (3 + 5)² = √(8)² = 8
• c = √(5 - 1)² + (-5 - 3)² = √16 + 64 = √80 = 4√5

Evaluating if it is right Δ by verifying Pythagorean Theorem :

• a² + b² = c²
• (4)² + (8)² = (4√5)²
• 16 + 64 = 80
• 80 = 80
• ⇒ ΔRST is a right triangle