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.
Accepted Solution
A:
Answer:Yes, the right angle is angle C.Step-by-step explanation:The given triangle has vertices at A(–2, 3), B(–3, –6), and C(2, –1).Recall the slope formula;[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]The slope of the line going through AC is [tex]m_{AC}=\frac{-1-3}{2--2}=-1[/tex]The slope of the line going through BC s [tex]m_{AC}=\frac{-1--6}{2--3}=1[/tex]The product of the slopes of AC and BC is [tex]-1\times1=-1[/tex]This means line AC is perpendicular to BC at C. Hence the triangle ABC is right angled at C.