# The coordinates of the vertices of triangle ABC are A(-1,3), B(1,2) and C(-3,-1). Determine the slope of each side of the triangle and use that information to determine if the triangle is a right triangle or not?

Jan 7, 2018

It’s a right triangle

#### Explanation:

Slope of AB ${m}_{A B} = \frac{2 - 3}{1 - \left(- 1\right)} = - \frac{1}{2}$

Slope of BC ${m}_{B C} = \frac{- 1 - 2}{- 3 - 1} = \frac{3}{4}$

Slope of CA ${m}_{C A} = \frac{- 1 - 3}{- 3 + 1} = 2$

${m}_{A B} \cdot {m}_{C A} = - \left(\frac{1}{2}\right) \cdot 2 = - 1$

Hence it’s a right triangle.