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How to Use the Midpoint Formula

Posted by Hayley Milliman | Aug 21, 2019 1:00:00 PM

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 A (X1, Y1) to B (X2, Y2) 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.

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First, you’ll want to find point A. The values for point A are X1 = -3 and Y1 = 2.

Next, you’ll want to find point B. The values for point B are X2 = 4 and Y2 = 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 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

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

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

(8, 5)

 

Final Thoughts

The midpoint formula allows you to find the exact midpoint of a line segment. The midpoint formula is $({X_1 + X_2}/2 , {Y_1+Y_2}/2)$.

 

What's Next?

Want to brush up on any of your other math topics ahead of the ACT? Check out our individual math guides to get the walk-through on each and every topic on the ACT math test.

Running out of time on the ACT math section? Our guide will help you learn how to beat the clock and maximize your ACT math score.

Running out of time on the SAT math section? Look no further than our guide to help you beat the clock and maximize your SAT math score.

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Hayley Milliman
About the Author

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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