How to Use the Midpoint Formula

The midpoint formula finds the point exactly halfway between two other points. It's one of the most straightforward formulas in coordinate geometry — and once you see what it's really doing, it becomes hard to forget.

The Formula

Given two points $(x_1, y_1)$ and $(x_2, y_2)$, the midpoint $M$ between them is:

$$M = \left(\frac{x_1 + x_2}{2},\ \frac{y_1 + y_2}{2}\right)$$

That's it. You're taking the average of the x-coordinates and the average of the y-coordinates. The midpoint is just the average of the two points — one dimension at a time.

This makes intuitive sense: the average of two numbers always lands between them, and the average of equal numbers is that number itself. So averaging x-coordinates gives you the x-value halfway between them, and averaging y-coordinates gives the y-value halfway between them.

Worked Examples

Example 1

Find the midpoint between $(2, 4)$ and $(8, 10)$.

$$M = \left(\frac{2 + 8}{2},\ \frac{4 + 10}{2}\right) = \left(\frac{10}{2},\ \frac{14}{2}\right) = (5, 7)$$

Quick check: 5 is between 2 and 8, and 7 is between 4 and 10. ✓

Example 2

Find the midpoint between $(-3, 5)$ and $(4, -9)$.

$$M = \left(\frac{-3 + 4}{2},\ \frac{5 + (-9)}{2}\right) = \left(\frac{1}{2},\ \frac{-4}{2}\right) = \left(0.5,\ -2\right)$$

Negative coordinates work exactly the same — just apply the formula.

Example 3

Find the midpoint between $(0, 0)$ and $(7, 3)$.

$$M = \left(\frac{0 + 7}{2},\ \frac{0 + 3}{2}\right) = \left(3.5,\ 1.5\right)$$

Example 4: Finding a Missing Endpoint

The midpoint formula can also work in reverse. If you know the midpoint and one endpoint, you can find the other.

Problem: One endpoint of a segment is $(1, 6)$. The midpoint is $(4, 2)$. Find the other endpoint.

Let the unknown endpoint be $(x, y)$. Set up the midpoint formula and solve each coordinate separately.

For x:

$$\frac{1 + x}{2} = 4 \implies 1 + x = 8 \implies x = 7$$

For y:

$$\frac{6 + y}{2} = 2 \implies 6 + y = 4 \implies y = -2$$

The missing endpoint is $(7, -2)$.

Check: Midpoint of $(1, 6)$ and $(7, -2)$: $\left(\frac{1+7}{2},\ \frac{6+(-2)}{2}\right) = (4, 2)$ ✓

Example 5

A diameter of a circle has endpoints $(-5, 1)$ and $(3, 7)$. Find the center of the circle.

The center of a circle is the midpoint of any diameter:

$$\text{center} = \left(\frac{-5 + 3}{2},\ \frac{1 + 7}{2}\right) = \left(\frac{-2}{2},\ \frac{8}{2}\right) = (-1, 4)$$

Midpoint Calculator

Enter the coordinates of both endpoints and the midpoint appears instantly.

Point 1

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Point 2

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Practice Problems

Find the midpoint between $(0, 0)$ and $(10, 6)$.

Show answer$M = \left(\frac{0+10}{2}, \frac{0+6}{2}\right) = (5, 3)$

Find the midpoint between $(-4, 3)$ and $(6, -1)$.

Show answer$M = \left(\frac{-4+6}{2}, \frac{3+(-1)}{2}\right) = \left(1, 1\right)$

Find the midpoint between $(3, -7)$ and $(-3, 7)$.

Show answer$M = \left(\frac{3+(-3)}{2}, \frac{-7+7}{2}\right) = (0, 0)$. The midpoint is the origin.

The midpoint between $(x, 5)$ and $(3, 1)$ is $(6, 3)$. Find $x$.

Show answerFor the x-coordinate: $\frac{x+3}{2} = 6 \implies x+3 = 12 \implies x = 9$.

One endpoint is $(-2, 8)$ and the midpoint is $(1, 3)$. Find the other endpoint.

Show answerFor x: $\frac{-2+x}{2} = 1 \implies x = 4$. For y: $\frac{8+y}{2} = 3 \implies y = -2$. The other endpoint is $(4, -2)$.

For a companion skill, see Length of a Line Segment — if you can find the midpoint, finding the full length using the Distance Formula is the natural next step.