Midpoint Formula

The midpoint of a segment is found one axis at a time: average the two x-coordinates for the midpoint's x, then average the two y-coordinates for its y. Worked example: the midpoint of (3, 4) and (11, −2) has x = (3 + 11)/2 = 7 and y = (4 + (−2))/2 = 1, giving (7, 1). Run this calculator twice, once per axis, and you have the point.

The rearrangements answer the question students actually get asked more often: "one end of a segment is at 2 and the midpoint is at 5 — where is the other end?" The answer is x₂ = 2(5) − 2 = 8, not 5 + 2. Doubling the midpoint is the whole trick, and forgetting to double is the single commonest error on this topic. The idea is as old as coordinates themselves — Descartes and Fermat, working independently in the 1630s, turned geometry into arithmetic precisely so that questions like this could be answered by averaging instead of by compass construction. Because both endpoints and the midpoint are lengths, you can mix units freely here: an endpoint in inches and a midpoint in feet convert before the arithmetic runs.