How do you find the midpoint of (-4,-5) and (1,-2)?

Mar 18, 2018

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

Explanation:

$\text{the coordinates of the midpoint are the average of}$
$\text{the coordinates of the endpoints}$

$\text{midpoint } = \left[\frac{1}{2} \left(- 4 + 1\right) , \frac{1}{2} \left(- 5 - 2\right)\right]$

$\textcolor{w h i t e}{\times \times \times x} = \left(- \frac{3}{2} , - \frac{7}{2}\right)$

Mar 18, 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:

$M = \left(\frac{\textcolor{red}{- 4} + \textcolor{b l u e}{1}}{2} , \frac{\textcolor{red}{- 5} + \textcolor{b l u e}{- 2}}{2}\right)$

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