# How do you find the midpoint of the segment with the endpoints (2/3,9/2) and (1/3,11/2)?

Jun 6, 2017

See a solution process below:

#### 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:

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

Substituting the values from the points in the problem gives:

$M = \left(\frac{\textcolor{red}{\frac{2}{3}} + \textcolor{b l u e}{\frac{1}{3}}}{2} , \frac{\textcolor{red}{\frac{9}{2}} + \textcolor{b l u e}{\frac{11}{2}}}{2}\right)$

$M = \left(\frac{\left(\frac{\textcolor{red}{2} + \textcolor{b l u e}{1}}{3}\right)}{2} , \frac{\frac{\textcolor{red}{9} + \textcolor{b l u e}{11}}{2}}{2}\right)$

$M = \left(\frac{\frac{3}{3}}{2} , \frac{\frac{20}{2}}{2}\right)$

$M = \left(\frac{1}{2} , \frac{10}{2}\right)$

$M = \left(\frac{1}{2} , 5\right)$