How to Find the Midpoint of Two Points: The Midpoint Formula

Imagine that you have two points on a coordinate plane and your teacher asks you to find the midpoint. This task requires a bit more work, because unlike a singular plane where you just add two points and divide by two, you have to find the center point of two planes, the x and y planes. Luckily there is a formula, the midpoint formula, and it looks like this:

Components

Let’s identify the components of the formula.

• (xm,ym)=midpoint coordinates

• (x1,y1)=first set of coordinates

• (x2,y2)=second set of coordinates

Practice Problems

Question 1

Find the midpoint between these two points.

The first step is identifying the components of the formula. It doesn’t matter which coordinate point you choose for the first and second set of coordinates. 

(x1,y1)= (4,3)

(x2,y2)= (12,7) 

Now, let’s plug this into the formula.

Then just solve like normal:

The midpoint is (8,5) which makes sense if you look at it on the graph.

This coordinate is right in the middle. 

Remember how it was mentioned that it didn’t matter which coordinate point you choose for the first and second set of coordinates? Let’s see why by switching the first and second set of coordinates. 

(x1,y1)= (12,7)

(x2,y2)= (4,3)

Now, let’s plug this into the formula.

Bam! Same answer🎊

Question 2

Find the midpoint between these two points.

The first step is identifying the components of the formula. 

(x1,y1)= (-4,2)

(x2,y2)= (10,9) 

Now let’s plug this into the formula:

Then, just solve like normal:

The midpoint is (3,5.5).

Sometimes your answer will be a decimal, and that is ok.

Question 3

Find the missing point using the following information:

(10,6)=midpoint coordinates

(4,5)=first set of coordinates

(x,7)=second set of coordinates 

In this practice you must find a missing point, however, you can use the midpoint formula to find the missing point. Just plug in all the information you have in the formula. 

(xm,ym)=(10,6) 

(x1,y1)= (4,5)

(x2,y2)= (x,7)

Then just solve like normal:

Pause! Here, we can eliminate a few things. We know the midpoint for the y is 6, so we can remove this segment to make things easier.

Now just solve for x. First multiply by 2 on both sides to get rid of the fraction.

Subtract 4 from both sides.

And just like that, we found the missing point.

Question 4

Find the missing coordinate point using the following information:

(8,3)=midpoint coordinates

(3,1)=first set of coordinates

(x,y)=second set of coordinates

In this practice you must find a missing coordinate, however, you can use the midpoint formula to find the missing coordinate. Just plug in all the information you have in the formula.

The first thing you can do is separate the x and y segments.

Now just solve for x. First, multiply by 2 on both sides to get rid of the fraction. Let’s start with the x part.

Subtract 3 from both sides.

Now let’s find the y point. First multiply by 2 on both sides to get rid of the fraction.

Subtract 1 from both sides.

There you go! We found that the missing coordinate is (13,5).

Conclusion

We did it! Midpoints aren’t as difficult as they sound, and we also learned that the midpoint formula can solve other problems.

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