What is the midpoint formula?

The midpoint formula is ((x1+x2)/2, (y1+y2)/2). It finds the coordinate point halfway between two endpoints.

Can the midpoint have decimals?

Yes. If the sum of the x-values or y-values is odd, the midpoint coordinate may be a decimal or fraction.

Is midpoint the same as distance?

No. Midpoint is a coordinate pair. Distance is the length between two points.

How do I check a midpoint answer?

Calculate the distance from the first endpoint to the midpoint and from the midpoint to the second endpoint. The distances should be equal.

Does midpoint work with negative coordinates?

Yes. Use the same formula and keep the negative signs when adding the coordinates.

What is the midpoint of a vertical line segment?

Average the y-values and keep the same x-value, because both endpoints have the same x-coordinate.

What is the midpoint of a horizontal line segment?

Average the x-values and keep the same y-value, because both endpoints have the same y-coordinate.

Why do we divide by 2?

Because the midpoint is the average of two x-values and the average of two y-values.

Education

Midpoint Formula Calculator

Find the midpoint between two points on the coordinate plane. Enter (x₁, y₁) and (x₂, y₂) to get the midpoint, distance, slope, and step-by-step formula substitution.

What the midpoint formula calculates

The midpoint is the point exactly halfway between two coordinate points. If the endpoints are (x₁, y₁) and (x₂, y₂), the midpoint is found by averaging the x-values and averaging the y-values. OpenStax presents the same idea in its distance and midpoint formulas lesson, where the midpoint is written as ((x₁+x₂)/2, (y₁+y₂)/2).

Midpoint = ((x₁ + x₂) ÷ 2, (y₁ + y₂) ÷ 2)

Worked example

Find the midpoint of A(-4, 7) and B(8, -1) x-coordinate: (-4 + 8) ÷ 2 = 4 ÷ 2 = 2 y-coordinate: (7 + -1) ÷ 2 = 6 ÷ 2 = 3 Midpoint = (2, 3)

This result means the point (2, 3) is the same distance from both endpoints. A quick check is to calculate the distance from A to the midpoint and from the midpoint to B; those two distances should match.

Common midpoint mistakes

Mistake	Correct approach
Adding all four numbers together	Average x-values separately and y-values separately.
Forgetting negative signs	Keep parentheses around negative coordinates.
Dividing the distance by 2	The midpoint is a coordinate pair, not only a length.

Common questions

The midpoint formula is ((x1+x2)/2, (y1+y2)/2). It finds the coordinate point halfway between two endpoints.
Yes. If the sum of the x-values or y-values is odd, the midpoint coordinate may be a decimal or fraction.
No. Midpoint is a coordinate pair. Distance is the length between two points.
Calculate the distance from the first endpoint to the midpoint and from the midpoint to the second endpoint. The distances should be equal.
Yes. Use the same formula and keep the negative signs when adding the coordinates.
Average the y-values and keep the same x-value, because both endpoints have the same x-coordinate.
Average the x-values and keep the same y-value, because both endpoints have the same y-coordinate.
Because the midpoint is the average of two x-values and the average of two y-values.