Chapter 13.2, Problem 21WE

To determine

To show that points $P,Q\text{ and }R$ are collinear by showing $\overline{PQ}$ and $\overline{QR}$ have the same slope.

Answer to Problem 21WE

It is proved that the points $P,Q\text{ and }R$ are collinear.

Explanation of Solution

Given:

The points are $P\left(-8,6\right),Q\left(-5,5\right)\text{ and }R\left(4,2\right)$.

Calculation:

Slope of a line when two points $\left(x_1,y_1\right)$ and $\left(x_2,y_2\right)$ are given is

  $m=\frac{y_2-y_1}{x_2-x_1}$

Points given are $P\left(-8,6\right),Q\left(-5,5\right)\text{ and }R\left(4,2\right)$

Slope of $\overline{PQ}$ :

  $\frac{y_2-y_1}{x_2-x_1}=\frac{5-6}{-5-\left(-8\right)}=\frac{-1}{3}=0.34$

Slope of $\overline{QR}$ :

  $\frac{y_2-y_1}{x_2-x_1}=\frac{2-5}{4-\left(-5\right)}=\frac{-3}{9}=-0.34$

Since, the slope of $\overline{PQ}$ is equals to slope of $\overline{QR}$ so thepoints $P,Q\text{ and }R$ are collinear.