Question

Triangle ABC has vertices at A(–2, 3), B(–3, –6), and C(2, –1). Is triangle ABC a right triangle? If so, which angle is the right angle?

No, the triangle has no right angles.
Yes, the right angle is angle A.
Yes, the right angle is angle B.
Yes, the right angle is angle C.

Answer 1

Yes — the right angle is angle C.

Reason: CA = A − C = (−4, 4) and CB = B − C = (−5, −5). Their dot product is (−4)(−5) + 4(−5) = 20 − 20 = 0, so CA ⟂ CB. Hence ∠C = 90°.