Chapter 13.2, Problem 20WE

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 20WE

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

Explanation of Solution

Given:

The points are $P\left(-1,3\right),Q\left(2,7\right)\text{ and }R\left(8,15\right)$.

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 $P\left(-1,3\right),Q\left(2,7\right)\text{ and }R\left(8,15\right)$

Slope of $\overline{PQ}$ :

  $\frac{y_2-y_1}{x_2-x_1}=\frac{7-3}{2-\left(-1\right)}=\frac{4}{3}=1.34$

Slope of $\overline{QR}$ :

  $\frac{y_2-y_1}{x_2-x_1}=\frac{15-7}{8-2}=\frac{8}{6}=1.34$

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