# What is the midpoint of the line segment between (10, 6) and (-4, 8)?

Feb 3, 2017

The midpoint is (3, 7)

#### Explanation:

The formula to find the mid-point of a line segment give the two end points is:

$M = \left(\frac{\textcolor{red}{{x}_{1}} + \textcolor{b l u e}{{x}_{2}}}{2} , \frac{\textcolor{red}{{y}_{1}} + \textcolor{b l u e}{{y}_{2}}}{2}\right)$

Where $M$ is the midpoint and the given points are:

($\textcolor{red}{\left({x}_{1} , {y}_{1}\right)}$) and ($\textcolor{b l u e}{\left({x}_{2} , {y}_{2}\right)}$)

Substituting the points from the problem and calculating gives:

$M = \left(\frac{\textcolor{red}{10} + \textcolor{b l u e}{- 4}}{2} , \frac{\textcolor{red}{6} + \textcolor{b l u e}{8}}{2}\right)$

$M = \left(\frac{6}{2} , \frac{14}{2}\right)$

$M = \left(3 , 7\right)$