Seeing Midpoint step by step
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.
Math calculator
Midpoint Calculator
Average corresponding coordinates to locate the center of a line segment. Beside midpoint, the output shows the operation used to obtain it.
Midpoint inputs
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The core relation in Midpoint
A midpoint lies halfway between two endpoints. Averaging the x-coordinates places it halfway horizontally; averaging the y-coordinates does the same vertically.
Checking Midpoint away from the browser
Review x₁ inside the Midpoint relation. Hold y₁ steady while testing x₂. A rough Midpoint gives Midpoint an independent scale check. Keep the revised Midpoint inputs beside their own Midpoint.
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.
Common interpretation traps for Midpoint
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.
Midpoint as equal division
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.
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.
Auditing the Midpoint result
Substitute the Midpoint solution into x₁. This Midpoint check rejects false Midpoint branches and forbidden denominators.
Choose an easy x₁ value before running Midpoint. Predict y₁, then compare it with the Midpoint output.
Reverse the Midpoint reasoning once: begin with the shown Midpoint and ask whether x₁ could produce it under y₁. When that Midpoint relationship fails, the contradiction narrows the error to an entry, order choice, or convention.
Midpoint: questions and answers
Must a midpoint have integer coordinates?
No. Odd coordinate sums produce halves, and decimal inputs may produce other decimals.
Can this work in three dimensions?
The same idea applies, but a 3D midpoint also averages the z-coordinates.
How can I verify it?
Vectors from the midpoint to the two endpoints should be opposites.