Chapter 8.3, Problem 37WE

To determine

To calculate: The slope of each line of a triangle whose vertices are,

  $A\left(-4,6\right),B\left(5,6\right),C\left(-4,-2\right)$

Answer to Problem 37WE

The slope of lines are:

  $\begin{array}{c}\overrightarrow{AB}=0\\ \overrightarrow{BC}=\frac{-8}{9}\end{array}$ .

Here the slope of $\overrightarrow{AC}$ has no slope.

Explanation of Solution

Given information:

The points of the lines:

  $A\left(-4,6\right),B\left(5,6\right),C\left(-4,-2\right)$

Formula used:

For finding the slope of the line:

  $m=\frac{y_2-y_1}{x_2-x_1}$ .

Calculation:

Consider the points,

  $A\left(-4,6\right),B\left(5,6\right),C\left(-4,-2\right)$

For finding the slope of line,

Apply the formula to find the slope a line of triangle $AB$ whose vertices are:

  $A\left(-4,6\right),B\left(5,6\right)$

  $m=\frac{y_2-y_1}{x_2-x_1}$

Now finding the values of $x_1,x_2,y_1,y_2$ from the points $A\left(-4,6\right),B\left(5,6\right)$ .

The values are:

  $\begin{array}{l}{x}_1=-4,y_1=6\\ x_2=5,y_2=6\end{array}$

Apply the values in the formula now:

  $\begin{array}{c}m=\frac{y_2-y_1}{x_2-x_1}\\ m=\frac{6-6}{5-\left(-4\right)}\\ m=\frac{0}{-9}\\ m=0\end{array}$

Apply the formula to find the slope a line of triangle $BC$ whose vertices are:

  $B\left(5,6\right),C\left(-4,-2\right)$

  $m=\frac{y_2-y_1}{x_2-x_1}$

Now finding the values of $x_1,x_2,y_1,y_2$ from the points $B\left(5,6\right),C\left(-4,-2\right)$ .

The values are:

  $\begin{array}{l}{x}_1=5,y_1=6\\ x_2=-4,y_2=-2\end{array}$

Apply the values in the formula now:

  $\begin{array}{c}m=\frac{y_2-y_1}{x_2-x_1}\\ m=\frac{2-6}{-4-5}\\ m=\frac{-8}{9}\end{array}$

Apply the formula to find the slope a line of triangle $AC$ whose vertices are:

  $A\left(-4,6\right),C\left(-4,-2\right)$

  $m=\frac{y_2-y_1}{x_2-x_1}$

Now finding the values of $x_1,x_2,y_1,y_2$ from the points $A\left(-4,6\right),C\left(-4,-2\right)$ .

The values are:

  $\begin{array}{l}{x}_1=-4,y_1=6\\ x_2=-4,y_2=-2\end{array}$

Apply the values in the formula now:

  $\begin{array}{c}m=\frac{y_2-y_1}{x_2-x_1}\\ m=\frac{-2-6}{-4-\left(-4\right)}\\ m=\frac{-8}{0}\\ m=-8\end{array}$

Here, The slope of lines are:

  $\begin{array}{c}\overrightarrow{AB}=0\\ \overrightarrow{BC}=\frac{-8}{9}\end{array}$ .

Here the slope of $\overrightarrow{AC}$ has no slope