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?

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

Answer 1

To determine if triangle ABC is a right triangle,

we can check if any of its angles form a right

angle. One way to do this is by analyzing the

slopes of the sides. If two sides have slopes

that multiply to -1, then those sides are

perpendicular, indicating the presence of

a right angle.

Let's find the slopes of the sides AB, BC, and

AC using the given coordinates:

1. Slope of AB (between A and B):

Slope = (y₂ - y₁) / (x₂ - x₁)

Slope AB = (-6 - 3) / (-3 - (-2)) = (-9) / (-1) = 9

2. Slope of BC (between B and C):

Slope BC = (-1 - (-6)) / (2 - (-3)) = (5) / (5) = 1

3. Slope of AC (between A and C):

Slope AC = (-1 - 3) / (2 - (-2)) = (-4) / (4) = -1

The product of the slopes of sides that would

form a right angle is 9 * (-1) = -9, which means

angles A and C are perpendicular. Therefore,

angle A in triangle ABC is the right angle.