Chapter 13.3, Problem 1WE

a.

To determine

To find the slope of line $\overleftrightarrow{AB}$ .

Answer to Problem 1WE

The slope of line $\overleftrightarrow{AB}$ is $\frac{2}{3}$ .

Explanation of Solution

Given:

The points are $A\left(-2,0\right)\text{ and }B\left(4,4\right)$

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 are $A\left(-2,0\right)\text{ and }B\left(4,4\right)$

Slope of line $\overleftrightarrow{AB}$

  $m_{AB}=\frac{4-0}{4-\left(-2\right)}=\frac{4}{6}=\frac{2}{3}$

Therefore, the slope of line $\overleftrightarrow{AB}$ is $\frac{2}{3}$ .

b.

To determine

To find the slope of any line parallel to $\overleftrightarrow{AB}$ .

Answer to Problem 1WE

The slope of any line parallel to $\overleftrightarrow{AB}$ is $\frac{2}{3}$ .

Explanation of Solution

Given:

The points are $A\left(-2,0\right)\text{ and }B\left(4,4\right)$

Calculation:

Since, the slope of two lines parallel to each other is same

Slope of line $\overleftrightarrow{AB}$

  $m_{AB}=\frac{4-0}{4-\left(-2\right)}=\frac{4}{6}=\frac{2}{3}$

Therefore, the slope of any line parallel to $\overleftrightarrow{AB}$ is $\frac{2}{3}$ .

c.

To determine

To find the slope of any line perpendicular to $\overleftrightarrow{AB}$ .

Answer to Problem 1WE

The slope any line perpendicular to $\overleftrightarrow{AB}$ is $-\frac{3}{2}$.

Explanation of Solution

Given:

The points are $A\left(-2,0\right)\text{ and }B\left(4,4\right)$

Calculation:

Since, the product of the slope of two lines perpendicular to each other $-1$ .

Consider slope of any line perpendicular to $\overleftrightarrow{AB}$ be $m_l$

Slope of line $\overleftrightarrow{AB}$

  $m_{AB}=\frac{4-0}{4-\left(-2\right)}=\frac{4}{6}=\frac{2}{3}=0.67$

Also,

  $\begin{array}{l}{m}_{AB}\times m_l=-1\\ \frac{2}{3}\times m_l=-1\\ m_l=-\frac{3}{2}\end{array}$

Therefore, the slope any line perpendicular to $\overleftrightarrow{AB}$ is $-\frac{3}{2}$