Chapter 13.2, Problem 12WE

To determine

To find the slope and length of the line $\overline{AB}$ .

Answer to Problem 12WE

The slope of line is $-3$ and length of the line $\overline{AB}$ is $2\sqrt{10}$ units.

Explanation of Solution

Given:

The coordinates of point $A,B$ are $\left(3,-1\right)\text{ and }\left(5,-7\right)$

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 given are $\left(3,-1\right)\text{ and }\left(5,-7\right)$

  $m=\frac{-7-\left(-1\right)}{\left(5\right)-\left(3\right)}=\frac{-6}{2}=-3$

Length of the line $\overline{AB}$ :

  $\sqrt{{\left(x_2-x_1\right)}^2+{\left(y_2-y_1\right)}^2}=\sqrt{{\left(5-3\right)}^2+{\left(-7-\left(-1\right)\right)}^2}=2\sqrt{10}$

Therefore , the slope of line is $-3$ and length of the line $\overline{AB}$ is $2\sqrt{10}$ units.