How do you find the midpoint of the segment connecting (3, 2) and (1, -2)?

Dec 26, 2016

The midpoint of this segment is (2, 0)

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 points we are given we can solve for $M$ as follows:

$M = \left(\frac{\textcolor{red}{3} + \textcolor{b l u e}{1}}{2} , \frac{\textcolor{red}{2} + \textcolor{b l u e}{\left(- 2\right)}}{2}\right)$

$M = \left(\frac{4}{2} , \frac{0}{2}\right)$

$M = \left(2 , 0\right)$