Point M is the midpoint between points A and B. If A is (-9, 2) and B is (-1,-8) where is M?

Mar 10, 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:

${M}_{A - B} = \left(\frac{\textcolor{red}{- 9} + \textcolor{b l u e}{- 1}}{2} , \frac{\textcolor{red}{2} + \textcolor{b l u e}{- 8}}{2}\right)$

${M}_{A - B} = \left(\frac{- 10}{2} , \frac{- 6}{2}\right)$

${M}_{A - B} = \left(- 5 , - 3\right)$