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

What is the formula for finding the midpoint of a line segment?

The midpoint formula is M = ((x₁ + x₂)/2, (y₁ + y₂)/2). In words, average the x-coordinates and average the y-coordinates of the two endpoints. For a segment from (2, 4) to (8, 10), the midpoint is ((2 + 8)/2, (4 + 10)/2) = (5, 7). The midpoint is always exactly the same distance from both endpoints.

How do you find the midpoint between two points?

Add the two x-values and divide by 2, then add the two y-values and divide by 2, and write the results as an ordered pair. For (−3, 6) and (5, −2), the x-coordinate is (−3 + 5)/2 = 1 and the y-coordinate is (6 + (−2))/2 = 2, so the midpoint is (1, 2). Midpoints can include fractions or decimals, such as (2.5, −1).

How do you find a missing endpoint using the midpoint?

Work the midpoint formula backward: double the midpoint’s coordinate and subtract the known endpoint’s coordinate. If the midpoint is (4, 1) and one endpoint is (1, −3), the other endpoint’s x is 2 × 4 − 1 = 7 and its y is 2 × 1 − (−3) = 5. So the missing endpoint is (7, 5). Check it: the average of (1, −3) and (7, 5) is (4, 1).

How do you find the midpoint of two numbers?

Add the two numbers and divide by 2. The midpoint of 14 and 30 is (14 + 30) ÷ 2 = 22, and the midpoint of −6 and 10 is (−6 + 10) ÷ 2 = 2. This is the same as finding their average, and it is exactly what the midpoint formula does separately for the x-coordinates and the y-coordinates of two points.

What is a midpoint in statistics?

In statistics, the midpoint, or class mark, of a class interval is the value halfway between its lower and upper limits. For the class 20 to 29, the midpoint is (20 + 29) ÷ 2 = 24.5. Midpoints help estimate the mean of grouped data in a frequency table: multiply each midpoint by its frequency, add the products and divide by the total frequency.

Why is finding the midpoint important?

Midpoints are useful whenever you need to split something evenly. In geometry, they help you bisect segments, find the center of a circle from the endpoints of a diameter, and show that a shape is a parallelogram, since its diagonals share a midpoint. For example, if a diameter runs from (−1, 2) to (7, 8), the circle’s center is ((−1 + 7)/2, (2 + 8)/2) = (3, 5).

Related Topics

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