Chapter 12, Problem 107CUR

To determine

To find: The midpoint of the segment with the given endpoints and then find the distance between the points.

Answer to Problem 107CUR

The midpoint of the segment is $\left(1,3\right)$ and the distance between the endpoints is $2\sqrt{193}$ .

Explanation of Solution

Given information: The end points of the segment $\left(8,15\right),\left(-6,-9\right)$

Calculation: Let’s find the midpoint of the segment with the endpoints $\left(8,15\right),\left(-6,-9\right)$ ,

The midpoint of the segment is,

  $\begin{array}{l}=\left(\frac{8-6}{2},\frac{15-9}{2}\right)\\ =\left(1,3\right)\end{array}$

Let’s find the distance between the points $\left(8,15\right),\left(-6,-9\right)$ ,

  $\begin{array}{l}=\sqrt{{\left(-6-8\right)}^2+{\left(-9-15\right)}^2}\\ =\sqrt{196+576}\\ =\sqrt{772}\\ =2\sqrt{193}\end{array}$

Hence, The midpoint of the segment is $\left(1,3\right)$ and the distance between the endpoints is

  $2\sqrt{193}$ .