# How do you find the midpoint of the line segment joining (2,-4) and (5,-2)?

##### 1 Answer
Jan 4, 2018

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:

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

$M = \left(\frac{7}{2} , - \frac{6}{2}\right)$

$M = \left(\frac{7}{2} , - 3\right)$