# What is the midpoint of the line segment that joins points (4,-2) and (-2,5)?

Dec 28, 2016

The midpoint is (1 , 3/2)

#### Explanation:

The equation 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 two points we are given in this problem gives:

$M = \left(\frac{\textcolor{red}{4} + \textcolor{b l u e}{- 2}}{2} , \frac{\textcolor{red}{- 2} + \textcolor{b l u e}{5}}{2}\right)$

$M = \left(\frac{2}{2} , \frac{3}{2}\right)$

$M = \left(1 , \frac{3}{2}\right)$