Chapter 13.2, Problem 14WE

To determine

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

Answer to Problem 14WE

The slope of line is $-0.18$ and length of the line $\overline{AB}$ is $5\sqrt{5}$ units.

Explanation of Solution

Given:

The coordinates of point $A,B$ are $\left(8,-7\right)\text{ and }\left(-3,-5\right)$

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 $\left(8,-7\right)\text{ and }\left(-3,-5\right)$

  $m=\frac{\left(-5\right)-\left(-7\right)}{\left(-3\right)-\left(8\right)}=\frac{2}{-11}=-0.18$

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

  $\sqrt{{\left(x_2-x_1\right)}^2+{\left(y_2-y_1\right)}^2}=\sqrt{{\left(-5-\left(-7\right)\right)}^2+{\left(-3-\left(8\right)\right)}^2}=\sqrt{125}=5\sqrt{5}$

Therefore , the slope of line is $-0.18$ and length of the line $\overline{AB}$ is $5\sqrt{5}$ units.