triangle abc has vertices at a(-2, 3), b(-3, -6), and c(2, -1). is triangle abc a right triangle? if so…

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?\nno, the triangle has no right angles.\nyes, the right angle is angle a.\nyes, the right angle is angle b.\nyes, the right angle is angle c.

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?\nno, the triangle has no right angles.\nyes, the right angle is angle a.\nyes, the right angle is angle b.\nyes, the right angle is angle c.

Answer

Explanation:

Step1: Find the slopes of the sides

The slope formula is $m = \frac{y_2 - y_1}{x_2 - x_1}$. Slope of $AB$: $m_{AB}=\frac{-6 - 3}{-3+2}=\frac{-9}{-1}=9$. Slope of $BC$: $m_{BC}=\frac{-1 + 6}{2+3}=\frac{5}{5}=1$. Slope of $AC$: $m_{AC}=\frac{-1 - 3}{2+2}=\frac{-4}{4}=-1$.

Step2: Check for perpendicular sides

Two lines are perpendicular if the product of their slopes is - 1. $m_{BC}\times m_{AC}=1\times(-1)=-1$.

Answer:

Yes, the right angle is angle C.