# How do you find the midpoint of A(-4,-2) and B(4,3)?

Jun 12, 2018

$\left(0 , \setminus \frac{1}{2}\right)$

#### Explanation:

Work out the centers of the x and the y coordinates individually such that the center is:

$\left(\setminus \frac{- 4 + 4}{2} , \setminus \frac{- 2 + 3}{2}\right)$

Simplify it to:
$\left(0 , \setminus \frac{1}{2}\right)$

Jun 12, 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:

$M = \left(\frac{\textcolor{red}{- 4} + \textcolor{b l u e}{4}}{2} , \frac{\textcolor{red}{- 2} + \textcolor{b l u e}{3}}{2}\right)$

$M = \left(\frac{0}{2} , \frac{1}{2}\right)$

$M = \left(0 , \frac{1}{2}\right)$