Chapter 13.5, Problem 8WE

To determine

To find: the length, slope, and midpoint of $\overline{PQ}$

Answer to Problem 8WE

The length is $\sqrt{116}$ , slope is $\frac{4}{10}$ and midpoint is $\left(2,6\right)$

Explanation of Solution

Given information: The points are $P\left(-3,4\right),Q\left(7,8\right)$

Calculation:

The midpoint of the segment that joins points $\left(x_1,y_1\right)\&\left(x_2,y_2\right)$ is the point

  $\begin{array}{l}M=\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)\\ M=\left(\frac{7-3}{2},\frac{8+4}{2}\right)\\ M=\left(\frac{4}{2},\frac{12}{2}\right)\\ M=\left(2,6\right)\end{array}$

The slope of $\overline{PQ}$

  $slope=\frac{y_2-y_1}{x_2-x_1}=\frac{8-4}{7-\left(-3\right)}=\frac{4}{10}$

The length of $\overline{PQ}$

  $\begin{array}{l}\overline{PQ}=\sqrt{{\left(x_2-x_1\right)}^2+{\left(y_2-y_1\right)}^2}\\ \overline{PQ}=\sqrt{{\left(7-\left(-3\right)\right)}^2+{\left(8-4\right)}^2}\\ \overline{PQ}=\sqrt{116}\end{array}$