How do I find an endpoint when I know the midpoint?

Rearrange the formula. If M = (2, 3) and one endpoint is (−2, 5), the other is (2×2 − (−2), 2×3 − 5) = (6, 1).

Is the midpoint the same as the average?

Yes — it is the average of the x-values paired with the average of the y-values. That is all the formula says.

Midpoint Calculator

The point halfway between two endpoints.

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Formula

M = ((x₁ + x₂) ÷ 2, (y₁ + y₂) ÷ 2)

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

The midpoint's x-coordinate is the average of the two x-coordinates, and its y-coordinate is the average of the two y-coordinates. It sits the same distance from each endpoint, which the page confirms by showing the half-length.

Worked example

For endpoints (−2, 5) and (6, 1): x = (−2 + 6) ÷ 2 = 2 and y = (5 + 1) ÷ 2 = 3, so the midpoint is (2, 3). The segment is about 8.9443 long, putting the midpoint 4.4721 from each end.

Where this can give the wrong answer

This is the midpoint of a straight segment on a flat plane. The halfway point between two places on Earth follows a curved path and needs a different calculation.
To find a missing endpoint instead, double the midpoint and subtract the known endpoint: x₂ = 2·Mx − x₁, and the same for y.
Add negative coordinates with their signs: the midpoint of −3 and −7 is −5, not 5.

FAQ

: Rearrange the formula. If M = (2, 3) and one endpoint is (−2, 5), the other is (2×2 − (−2), 2×3 − 5) = (6, 1).

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