Chapter 12, Problem 106CUR

To determine

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

Answer to Problem 106CUR

The midpoint of the segment is $\left(2,6\right)$ and the distance between the endpoints is $2\sqrt{5}$ .

Explanation of Solution

Given information: The end points of the segment $\left(4,7\right),\left(0,5\right)$

Calculation: Let’s find the midpoint of the segment with the endpoints $\left(4,7\right),\left(0,5\right)$ ,

The midpoint of the segment is,

  $\begin{array}{l}=\left(\frac{4+0}{2},\frac{7+5}{2}\right)\\ =\left(2,6\right)\end{array}$

Let’s find the distance between the points $\left(4,7\right),\left(0,5\right)$ ,

  $\begin{array}{l}=\sqrt{{\left(0-4\right)}^2+{\left(5-7\right)}^2}\\ =\sqrt{16+4}\\ =2\sqrt{5}\end{array}$

Hence, The midpoint of the segment is $\left(2,6\right)$ and the distance between the endpoints is $2\sqrt{5}$ .