In this video, you will learn the midpoint formula and how to use the midpoint formula to calculate the midpoint of a line segment if the two endpoints are known. Also, you will learn how to calculate the coordinates of an endpoint if the midpoint and the other endpoint is given.

## What is the midpoint formula?

The midpoint formula is based on the average of the x-coordinates and the average of the y-coordinates. The formula is used to find the coordinates of the midpoint of a line segment in the x-y plane.

**Midpoint Formula:**

In other words, we are simply finding the average of the two x-values and the two y-values.

To better understand how to apply the formula, let’s take a look at a couple of midpoint formula problems.

**For example:**

Given points and , find the midpoint.

By using the midpoint formula, substitute each value into the formulahttps://caddellprep.com/subjects/common-core-geometry/midpoint-formula/?preview=true

Combine like terms

Divide each expression

Let’s try an example where only one endpoint and the midpoint is given. In this problem we will find the other endpoint.

**For example:**

is the midpoint of . The coordinates of are and the coordinates of are . Find the coordinates of .

Like the previous example, substitute the x and the y-values.

Separate the equation to solve for *x* and *y* individually

x

y

## Video-Lesson Transcript

Let’s go over the midpoint formula.

We have two points – and in the -system.

The midpoint is the point in the middle of these two points.

Remember, and is a line segment each with corresponding and coordinates. So the midpoint also has and coordinates.

Let’s call the coordinates of as and . Likewise, coordinates are and .

The midpoint has the same distance not only between and but also between the two -coordinates and -coordinates.

Let’s call the midpoint coordinates as and . Midpoint coordinates are the average of the two coordinates.

So our formula is:

For example:

Let’s find the midpoint of a line segment which has point with coordinates and point with coordinates.

Let’s use our formula – average of the two coordinates and the two coordinates.

Let’s label the coordinates first so we won’t be confused.

Then substitute the given

So our midpoint is

This is just a coincidence that we came up with an identical value. But we can come up with any value for the – and -coordinates.

Just follow the formula.

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