How to Use the Midpoint Formula




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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

(X

1

, Y

1

) to

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

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

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


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?


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.


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