How do you find the midpoint of (2/5,-1/5), (1/3,5/2)?

Jun 27, 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 $\left(\textcolor{b l u e}{{x}_{2}} , \textcolor{b l u e}{{y}_{2}}\right)$

Substituting the values from the points in the problem gives:

$M = \left(\frac{\textcolor{red}{\frac{2}{5}} + \textcolor{b l u e}{\frac{1}{3}}}{2} , \frac{\textcolor{red}{- \frac{1}{5}} + \textcolor{b l u e}{\frac{5}{2}}}{2}\right)$

$M = \left(\frac{\left(\frac{3}{3} \times \textcolor{red}{\frac{2}{5}}\right) + \left(\frac{5}{5} \times \textcolor{b l u e}{\frac{1}{3}}\right)}{2} , \frac{\left(\frac{2}{2} \times \textcolor{red}{- \frac{1}{5}}\right) + \left(\frac{5}{5} \times \textcolor{b l u e}{\frac{5}{2}}\right)}{2}\right)$

$M = \left(\frac{\frac{6}{15} + \frac{5}{15}}{2} , \frac{- \frac{2}{10} + \frac{25}{10}}{2}\right)$

$M = \left(\frac{\frac{11}{15}}{2} , \frac{- \frac{23}{10}}{2}\right)$

$M = \left(\frac{11}{15 \times 2} , - \frac{23}{10 \times 2}\right)$

$M = \left(\frac{11}{30} , - \frac{23}{20}\right)$