Chapter 13.3, Problem 10WE

To determine

To show that $\Delta RST$ is a right triangle.

Explanation of Solution

Given information: the points are,

  $R\left(-1,1\right)S\left(2,4\right)T\left(5,1\right)$ .

Proof: The required proof is obtained as,

Product of the slopes of $\overline{RS}$ and $\overline{ST}$ are -1.

The slopes of $\overline{RS}=\frac{1-\left(4\right)}{-1-\left(2\right)}=\frac{-3}{-3}=1$

The slopes of $\overline{ST}=\frac{4-1}{2-5}=\frac{3}{-3}=-1$

Therefore, the $\angle RST$ is right angle.

Hence it is right angled triangle.