Chapter 12, Problem 108CUR

To determine

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

Answer to Problem 108CUR

The midpoint of the segment is $\left(7,-7\right)$ and the distance between the endpoints is $2\sqrt{29}$ .

Explanation of Solution

Given information: The end points of the segment $\left(9,-2\right),\left(5,-12\right)$

Calculation: Let’s find the midpoint of the segment with the endpoints $\left(9,-2\right),\left(5,-12\right)$ ,

The midpoint of the segment is,

  $\begin{array}{l}=\left(\frac{9+5}{2},\frac{-2-12}{2}\right)\\ =\left(7,-7\right)\end{array}$

Let’s find the distance between the points $\left(9,-2\right),\left(5,-12\right)$ ,

  $\begin{array}{l}=\sqrt{{\left(5-9\right)}^2+{\left(-12+2\right)}^2}\\ =\sqrt{16+100}\\ =\sqrt{116}\\ =2\sqrt{29}\end{array}$

Hence, The midpoint of the segment is $\left(7,-7\right)$ and the distance between the endpoints is $2\sqrt{29}$ .