How to Find Midpoint? (+FREE Worksheet!)

Finding the midpoint of a line segment means locating the exact point that lies halfway between two given endpoints. The midpoint formula is one of the most useful tools in coordinate geometry, appearing in everything from bisecting line segments to proving geometric theorems. With a simple formula and a bit of arithmetic, you can find any midpoint in seconds.

What Is the Midpoint?

The midpoint of a line segment is the point that divides it into two equal halves. On a coordinate plane, if you have two points \(\color{blue}{(x_{1}, y_{1})}\) and \(\color{blue}{(x_{2}, y_{2})}\), the midpoint \(\color{blue}{M}\) is found by averaging the \(\color{blue}{x}\)-coordinates and the \(\color{blue}{y}\)-coordinates separately:

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M =  (\(\color{blue}{\frac{(x<\text{ sub }>1 + x<\text{ sub }>2)}{2}}\),  \(\color{blue}{\frac{(y<\text{ sub }>1 + y<\text{ sub }>2)}{2}}\))

How to Use the Midpoint Formula

Step 1: Label the coordinates

Identify \(\color{blue}{(x_{1}, y_{1})}\) as the first point and \(\color{blue}{(x_{2}, y_{2})}\) as the second point. The labeling does not affect the answer.

Step 2: Add the x-coordinates and divide by 2

\(\color{blue}{M_{x} = \frac{(x_{1} + x_{2})}{2}}\)

Step 3: Add the y-coordinates and divide by 2

\(\color{blue}{M_{y} = \frac{(y_{1} + y_{2})}{2}}\)

Step 4: Write the midpoint as an ordered pair

\(\color{blue}{M = (M_{x}, M_{y})}\)

Step-by-Step Summary

1. Write down both endpoints.
2. Add the two \(\color{blue}{x}\)-values; divide by 2.
3. Add the two \(\color{blue}{y}\)-values; divide by 2.
4. Write the result as an ordered pair \(\color{blue}{(M_{x}, M_{y})}\).

Watch: Finding the Midpoint Formula (Video Lesson)

Khan Academy introduces the midpoint formula with a coordinate grid example:

Finding Midpoint – Worked Examples

Example 1: Find the midpoint of \(\color{blue}{(2, 3)}\) and \(\color{blue}{(6, 7)}\).

\(\color{blue}{M_{x} = \frac{(2 + 6)}{2} = 4}\).  \(\color{blue}{M_{y} = \frac{(3 + 7)}{2} = 5}\).
Answer: \(\color{blue}{M = (4, 5)}\)

Example 2: Find the midpoint of \(\color{blue}{(-1, 4)}\) and \(\color{blue}{(5, 2)}\).

\(\color{blue}{M_{x} = \frac{(-1 + 5)}{2} = \frac{4}{2} = 2}\).  \(\color{blue}{M_{y} = \frac{(4 + 2)}{2} = 3}\).
Answer: \(\color{blue}{M = (2, 3)}\)

Example 3: Find the midpoint of \(\color{blue}{(0, -3)}\) and \(\color{blue}{(4, 7)}\).

\(\color{blue}{M_{x} = \frac{(0 + 4)}{2} = 2}\).  \(\color{blue}{M_{y} = \frac{(-3 + 7)}{2} = 2}\).
Answer: \(\color{blue}{M = (2, 2)}\)

Example 4: Find the midpoint of \(\color{blue}{(-3, -5)}\) and \(\color{blue}{(3, 1)}\).

\(\color{blue}{M_{x} = \frac{(-3 + 3)}{2} = 0}\).  \(\color{blue}{M_{y} = \frac{(-5 + 1)}{2} = -2}\).
Answer: \(\color{blue}{M = (0, -2)}\)

More Practice: Midpoint Formula Video

This step-by-step video demonstrates finding the midpoint between two points with additional examples:

Exercises for Finding the Midpoint

Find the midpoint of each pair of points.

1. \(\color{blue}{(1, 2)}\) and \(\color{blue}{(7, 8)}\)
2. \(\color{blue}{(-2, 0)}\) and \(\color{blue}{(4, 6)}\)
3. \(\color{blue}{(3, -4)}\) and \(\color{blue}{(-1, 2)}\)
4. \(\color{blue}{(0, 0)}\) and \(\color{blue}{(8, 6)}\)
5. \(\color{blue}{(-5, 3)}\) and \(\color{blue}{(1, -7)}\)
6. \(\color{blue}{(2, 9)}\) and \(\color{blue}{(6, 1)}\)

Answers

1. \(\color{blue}{(4, 5)}\)
2. \(\color{blue}{(1, 3)}\)
3. \(\color{blue}{(1, -1)}\)
4. \(\color{blue}{(4, 3)}\)
5. \(\color{blue}{(-2, -2)}\)
6. \(\color{blue}{(4, 5)}\)

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Want More Practice?

We haven’t published a worksheet built specifically for Finding Midpoint just yet. In the meantime, the free worksheets below cover closely related skills and concepts. If you’d like extra practice, download any that look helpful, complete the problems, and check your work — they’re a great way to reinforce what you learned on this page and strengthen the foundations this topic builds on:

• Download Slope and Rate of Change Worksheet
• Download Writing Linear Equations from Graphs and Tables Worksheet

Frequently Asked Questions

Why do we average the coordinates to find the midpoint?

The average of two values on a number line gives you the point exactly halfway between them. Doing this separately for both the \(\color{blue}{x}\)- and \(\color{blue}{y}\)-coordinates gives the midpoint of the segment in 2D.

Does it matter which point I call (x₁, y₁) and which I call (x₂, y₂)?

No. Addition is commutative: \(\color{blue}{\frac{(x_{1} + x_{2})}{2} = \frac{(x_{2} + x_{1})}{2}}\). Either labeling gives the same midpoint.

Can I use the midpoint formula with negative coordinates?

Yes. Treat negative coordinates as signed numbers. For example, the midpoint of \(\color{blue}{(-4, 2)}\) and \(\color{blue}{(2, 8)}\) is \(\color{blue}{(\frac{(-4+2)}{2}, \frac{(2+8)}{2}) = (-1, 5)}\).

Related Topics

• Finding Distance of Two Points
• One-Step Equations
• Multi-Step Equations
• Evaluating Two Variables
• Slope of a Line