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## High school geometry

### Course: High school geometry>Unit 6

Lesson 1: Distance and midpoints

# Midpoint formula review

Review the midpoint formula and how to apply it to solve problems.

## What is the midpoint formula?

The formula gives the midpoint of the points $\left({x}_{1},{y}_{1}\right)$ and $\left({x}_{2},{y}_{2}\right)$ in the coordinate plane:
$\left(\frac{{x}_{1}+{x}_{2}}{2},\frac{{y}_{1}+{y}_{2}}{2}\right)$

## What problems can I solve with the midpoint formula?

Given two points on the plane, you can find their midpoint. For example, let's find the midpoint of $\left(5,3\right)$ and $\left(1,7\right)$:
$\begin{array}{rl}& \phantom{=}\left(\frac{{x}_{1}+{x}_{2}}{2},\frac{{y}_{1}+{y}_{2}}{2}\right)\\ \\ & =\left(\frac{5+1}{2},\frac{3+7}{2}\right)\phantom{\rule{1em}{0ex}}\text{Plug in coordinates}\\ \\ & =\left(3,5\right)\end{array}$
Notice: we were careful to put the $x$-coordinates together and the $y$-coordinates together and not mix them up.

What is the midpoint of $\left(6,2\right)$ and $\left(10,0\right)$?