How do you find the midpoint of (-5, 4) and (3, 2)?

Apr 30, 2017

See the 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:

$\left(\textcolor{red}{\left({x}_{1} , {y}_{1}\right)}\right)$ and $\left(\textcolor{b l u e}{\left({x}_{2} , {y}_{2}\right)}\right)$

Substituting the values from the points in the problem gives:

$M = \left(\frac{\textcolor{red}{- 5} + \textcolor{b l u e}{3}}{2} , \frac{\textcolor{red}{4} + \textcolor{b l u e}{2}}{2}\right)$

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

$M = \left(- 1 , 3\right)$

Apr 30, 2017

Use the formulas:
x_"midpoint"=(x_"start"+x_"end")/2
y_"midpoint"=(y_"start"+y_"end")/2

Explanation:

Given the start point $\left(- 5 , 4\right)$ and the end point $\left(3 , 2\right)$:

${x}_{\text{midpoint}} = \frac{- 5 + 3}{2} = \frac{- 2}{2} = - 1$
${y}_{\text{midpoint}} = \frac{4 + 2}{2} = \frac{6}{2} = 3$

The midpoint is: $\left(- 1 , 3\right)$