Chapter 13.2, Problem 7CE

a.

To determine

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

Answer to Problem 7CE

The slope of $\overleftrightarrow{AB}$ is $1.5$ .

Explanation of Solution

Given:

Below is the figure given

  

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 $A\left(1,0\right)$ and $B\left(3,3\right)$

  $m=\frac{3-0}{\left(3\right)-\left(1\right)}=\frac{3}{2}=1.5$

Therefore, the slope of $\overleftrightarrow{AB}$ is $1.5$

b.

To determine

To find the $\tan n^{\circ }$ .

Answer to Problem 7CE

The value of $\tan n^{\circ }$ is $1.5$

Explanation of Solution

Given:

Below is the figure given

  

Calculation:

Slope of a line when two points $\left(x_1,y_1\right)$ and $\left(x_2,y_2\right)$ are given is

  $\tan \theta =m=\frac{y_2-y_1}{x_2-x_1}$

Where $\theta$ is the angle which lines makes with positive direction of $x-\text{axis}$

Points given are $A\left(1,0\right)$ and $B\left(3,3\right)$

  $\begin{array}{l}\tan n^{\circ }=m=\frac{3-0}{\left(3\right)-\left(1\right)}=\frac{3}{2}=1.5\\ \tan n^{\circ }=1.5\end{array}$

Therefore, the value of $\tan n^{\circ }$ is $1.5$ .

c.

To determine

To tell whether the statement is true or false and explain.

Answer to Problem 7CE

Thestatement is true.

Explanation of Solution

Given:

The statement is

If a line with positive slope makes an acute angle of $n^{\circ }$ with the $x-\text{axis}$ ,then the slope of the line is $\tan n^{\circ }$ .

Below is the figure given

  

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 $A\left(1,0\right)$ and $B\left(3,3\right)$

  $m=\frac{3-0}{\left(3\right)-\left(1\right)}=\frac{3}{2}=1.5$

Also ,

  $\tan n^{\circ }=\frac{\text{Perpendicular}}{\text{Base}}=\frac{3}{2}=1.5$

Therefore, the above statement is true.