Chapter 13.1, Problem 22PSC

To determine

To verify: That the slope of $\overleftrightarrow{\text{AC}}$ is $-\frac{2}{3}$ .

Answer to Problem 22PSC

It is verified that the slope of $\overline{\text{AC}}$ is also $-\frac{2}{3}$ .

Explanation of Solution

Given:

It is given that $A=\left(10,1\right)$ and $B=\left(2,9\right)$

Calculation:

Consider the following figure.

  

Find the slope of $\overline{AB\text{'}}$ .

Substitute $-2$ for $x_1$ , 10 for $x_2$ , 1 for $y_2$ and 9 for $y_1$ in the equation $m=\frac{y_2-y_1}{x_2-x_1}$ .

  $\begin{array}{c}{m}_r=\frac{1-9}{10+2}\\ =-\frac{2}{3}\end{array}$

So, slope of $\overline{\text{AC}}$ is also $-\frac{2}{3}$ , since $A$ , $C$ ,and $B\text{'}$ are collinear.

Therefore, it is verified that the slope of $\overline{\text{AC}}$ is also $-\frac{2}{3}$ .