Average corresponding coordinates to locate the center of a line segment. Beside midpoint, the output shows the operation used to obtain it.
Midpoints help bisect segments, find circle centers from diameter endpoints, create balanced coordinates, and divide a trip or design line into equal straight-line halves. A related application of Midpoint is segment slope.
A midpoint lies halfway between two endpoints. Averaging the x-coordinates places it halfway horizontally; averaging the y-coordinates does the same vertically.
For this page, midpoint is interpreted under the stated convention and input order.
The midpoint of (−6, 2) and (10, 8) is ((−6 + 10)/2, (2 + 8)/2) = (2, 5). Each endpoint is the same distance from that point.
Add the endpoint x-values and divide by 2. Repeat with the endpoint y-values. Check by comparing the coordinate changes from the midpoint to each endpoint. A hand-worked extension of Midpoint is segment length.
Do not cross-pair x with y. The two averages are independent. A midpoint can contain halves or other decimals even when all endpoint coordinates are integers.
Review the sign, scale, and unit of midpoint after entering x₁, y₁, x₂ and y₂.
The cleanest input audit is to restate the problem using x₁, y₁, x₂ and y₂. If that sentence sounds wrong, correct the assignment before asking for midpoint.
Moving one endpoint by a given vector moves the midpoint by half that vector. Swapping endpoints changes nothing because coordinate averaging is symmetric. The pattern also provides a quick estimate of whether a revised result is plausible.
The midpoint bisects one segment. It should not be confused with a dataset mean unless the dataset consists exactly of the two endpoints considered coordinate by coordinate. The wording of the problem should decide which operation is appropriate.
The formula and result serve different readers: the formula shows what was done, and the rounded midpoint communicates scale. Keep both when the work needs review.
A screenshot is unnecessary when x₁, y₁, x₂ and y₂ and the shown formula are saved in plain text. Include the rounding rule if the reported midpoint is approximate.
A midpoint is also a ratio point: it divides the segment in the ratio 1:1. More general section formulas replace the equal halves with a chosen ratio, but the coordinate-averaging shortcut belongs specifically to equal division.
The result can verify symmetry in a drawing. Reflecting either endpoint across the midpoint should land exactly on the other endpoint; coordinate differences from the center will have equal magnitudes and opposite signs.
No. Odd coordinate sums produce halves, and decimal inputs may produce other decimals.
The same idea applies, but a 3D midpoint also averages the z-coordinates.
Vectors from the midpoint to the two endpoints should be opposites.