---
title: How to Use the Midpoint Formula · PrepScholar
description: What is the midpoint formula? Check out our complete guide with midpoint formula examples.
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---

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# [How to Use the Midpoint Formula](https://blog.prepscholar.com/midpoint-formula)

![author image](https://cdn2.hubspot.net/hubfs/360031/hayley.jpg)

Posted by [Hayley Milliman](https://blog.prepscholar.com/author/hayley-milliman) | Updated on September 24, 2024

[General Education](https://blog.prepscholar.com/topic/general-education)

 

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**The midpoint formula lets you find the exact center between two defined points.** You might encounter this formula in your economics or geometry class or while prepping for a college entrance exam like the SAT or ACT.

In this article, we’ll answer the questions what is the midpoint formula and when do you use the midpoint formula, as well as provide example problems you can try.

 

## What Is The Midpoint Formula in Geometry?

You can probably guess what the midpoint formula does based on its name: **the midpoint formula helps you find the exact halfway between two defined points.** That halfway mark is the midpoint.

Here’s the actual midpoint formula:

The midpoint $N$ of the line segment between points $A$ $(X\_1, Y\_1)$ and $B $(X\_2, Y\_2)$ can be found with the formula:

$$({X\_1 + X\_2}/2 , {Y\_1+Y\_2}/2)$$

Let’s take a look at that in practice.

![pasted image 0](https://360031.fs1.hubspotusercontent-na1.net/hub/360031/hubfs/pasted%20image%200.png?width=499&name=pasted%20image%200.png)

First, you’ll want to find point $A$. The values for point $A$ are $X\_1 = -3$ and $Y\_1 = 2$.

Next, you’ll want to find point $B$. The values for point $B$ are $X\_2 = 4$ and $Y\_2 = 4$.

Now that we have those values, we plug them into our equation:

$$({\\-3 + 4}/2, {\\2 + 4}/2)$$

$$(1/2, 6/2) = (1/2, 3)$$

The exact midpoint of the line segment $\\ov{AB}$ is $(1/2, 3)$.

 

## Midpoint Formula Geometry Examples

Here are several examples of midpoint formula geometry problems.

 

### Problem #1

A line segment has the endpoints $B$ $(4, 5)$ and $F$ $(2, 1)$. Find the coordinates of its midpoint $M$.

 

$M = ({\\4+ 2}/{\\2} , {\\5 + 1}/{\\2})$

$= (6/2 , 6/2)$

$= (3,3)$

### Problem #2

![graph2](https://360031.fs1.hubspotusercontent-na1.net/hub/360031/hubfs/graph2.png?width=500&name=graph2.png)

 

$M = ({\\5+ -2}/{\\2}, {\\4 + 1}/{\\2})$

$= (3/2, 5/2)$

 

### Problem #3

*CD* has endpoints at *C* $(9, 1)$ and *D* $(7, 9)$. Find the midpoint *M* of *CD*.

$M = ({\\9+ 7}/{\\2}, {\\9 + 1}/{\\2})$

$M = (16/2, 10/2)$

$M = (8, 5)$

 

## Final Thoughts

The midpoint formula allows you to find the exact midpoint of a line segment. The midpoint formula is $({X\_1 + X\_2}/2 , {Y\_1+Y\_2}/2)$.

 

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 Hayley Milliman

 Hayley Milliman is a former teacher turned writer who blogs about education, history, and technology. When she was a teacher, Hayley's students regularly scored in the 99th percentile thanks to her passion for making topics digestible and accessible. In addition to her work for PrepScholar, Hayley is the author of Museum Hack's Guide to History's Fiercest Females.

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