Chapter 13.3, Problem 2WE

a.

To determine

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

Answer to Problem 2WE

The slope of line $\overleftrightarrow{AB}$ is $-\frac{2}{5}$ .

Explanation of Solution

Given:

The points are $A\left(-3,1\right)\text{ and }B\left(2,-1\right)$

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 $A\left(-3,1\right)\text{ and }B\left(2,-1\right)$

Slope of line $\overleftrightarrow{AB}$

  $m_{AB}=\frac{-1-1}{2-\left(-3\right)}=-\frac{2}{5}$

Therefore, the slope of line $\overleftrightarrow{AB}$ is $-\frac{2}{5}$ .

b.

To determine

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

Answer to Problem 2WE

The slope of any line parallel to $\overleftrightarrow{AB}$ is $-\frac{2}{5}$ .

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 $\overleftrightarrow{AB}$

  $m_{AB}=\frac{-1-1}{2-\left(-3\right)}=-\frac{2}{5}$

Therefore, the slope of any line parallel to $\overleftrightarrow{AB}$ is $-\frac{2}{5}$ .

c.

To determine

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

Answer to Problem 2WE

The slope any line perpendicular to $\overleftrightarrow{AB}$ is $\frac{5}{2}$.

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 $m_l$

points are $A\left(-3,1\right)\text{ and }B\left(2,-1\right)$

Slope of line $\overleftrightarrow{AB}$

  $m_{AB}=\frac{-1-1}{2-\left(-3\right)}=-\frac{2}{5}$ Also,

  $\begin{array}{l}{m}_{AB}\times m_l=-1\\ -\frac{2}{5}\times m_l=-1\\ m_l=\frac{5}{2}\end{array}$

Therefore, the slope any line perpendicular to $\overleftrightarrow{AB}$ is $\frac{5}{2}$