How it works
The midpoint of a line segment is the point exactly halfway between its endpoints. Each coordinate is simply the average of the two endpoints' coordinates.
It is used to find the center of a circle from a diameter's endpoints, to bisect segments in geometry, and to find the point halfway between two locations on a grid.
Formula
M = ((x₁ + x₂)/2, (y₁ + y₂)/2) (3D: add (z₁ + z₂)/2)
Questions people ask
How do I find an endpoint if I know the midpoint?
Double the midpoint and subtract the known endpoint: x₂ = 2·Mx − x₁, and likewise for y.
Is the midpoint always on the segment?
Yes. It lies on the segment and is equidistant from both endpoints.
What is the perpendicular bisector?
The line through the midpoint at right angles to the segment. Its slope is the negative reciprocal of the segment's slope.