Chapter 12, Problem 109CUR

To determine

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

Answer to Problem 109CUR

The midpoint of the segment is $\left(5.5,-5.5\right)$ and the distance between the endpoints is $6\sqrt{3}$ .

Explanation of Solution

Given information: The end points of the segment $\left(-4,10\right),\left(-7,1\right)$

Calculation: Let’s find the midpoint of the segment with the endpoints $\left(-4,10\right),\left(-7,1\right)$ ,

The midpoint of the segment is,

  $\begin{array}{l}=\left(\frac{-4-7}{2},\frac{10+1}{2}\right)\\ =\left(5.5,-5.5\right)\end{array}$

Let’s find the distance between the points $\left(-4,10\right),\left(-7,1\right)$ ,

  $\begin{array}{l}=\sqrt{{\left(-7+4\right)}^2+{\left(1-10\right)}^2}\\ =\sqrt{9+99}\\ =\sqrt{108}\\ =6\sqrt{3}\end{array}$

Hence, The midpoint of the segment is $\left(5.5,-5.5\right)$ and the distance between the endpoints is $6\sqrt{3}$ .