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## Geometry (all content)

### Course: Geometry (all content)>Unit 15

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 parenthesis, start color #1fab54, x, start subscript, 1, end subscript, end color #1fab54, comma, start color #e07d10, y, start subscript, 1, end subscript, end color #e07d10, right parenthesis and left parenthesis, start color #1fab54, x, start subscript, 2, end subscript, end color #1fab54, comma, start color #e07d10, y, start subscript, 2, end subscript, end color #e07d10, right parenthesis in the coordinate plane:
left parenthesis, start color #1fab54, start fraction, x, start subscript, 1, end subscript, plus, x, start subscript, 2, end subscript, divided by, 2, end fraction, end color #1fab54, comma, start color #e07d10, start fraction, y, start subscript, 1, end subscript, plus, y, start subscript, 2, end subscript, divided by, 2, end fraction, end color #e07d10, right parenthesis
The first quadrant of a coordinate plane with three tick marks on the x axis labeled x one, x one plus x two all divided by two, and x two. There are three tick marks on the y axis labeled y one, y one plus y two all divided by two, and y two. There is a point at x one, y one and another point at x two, y two. A third point is the midpoint of the two others at x one plus x two all divided by two, y one plus y two all divided by two.

## 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 parenthesis, start color #1fab54, 5, end color #1fab54, comma, start color #e07d10, 3, end color #e07d10, right parenthesis and left parenthesis, start color #1fab54, 1, end color #1fab54, comma, start color #e07d10, 7, end color #e07d10, right parenthesis:
\begin{aligned} &\phantom{=}\left(\greenD{\dfrac{x_1+x_2}{2}}, \goldD{\dfrac{y_1+y_2}{2}}\right) \\\\ &=\left(\greenD{\dfrac{5+1}{2}}, \goldD{\dfrac{3+7}{2}}\right)\quad\small\gray{\text{Plug in coordinates}} \\\\ &=(\greenD3, \goldD5) \end{aligned}
Notice: we were careful to put the x-coordinates together and the y-coordinates together and not mix them up.