A triangle has vertices A(1, 1), B(5, 3) and C(-2, 7). Its three side lengths show that it is right-angled. At which vertex is the right angle?

Question

Accepted Answer

At A, because AB^2 + AC^2 = BC^2. AB^2 = (5-1)^2 + (3-1)^2 = 20, AC^2 = (-2-1)^2 + (7-1)^2 = 45, BC^2 = (-2-5)^2 + (7-3)^2 = 65. Since 20 + 45 = 65, the two shorter sides AB = 2√5 and AC = 3√5 meet at A, so the right angle is at A and BC = √65 is the hypotenuse. Choosing B or C means testing the wrong pair of sides.

A triangle has vertices A(1, 1), B(5, 3) and C(-2, 7). Its three side lengths show that it is right-angled. At which vertex is the right angle?

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