The formula
M = ((x₁ + x₂) ÷ 2, (y₁ + y₂) ÷ 2)
Why it works
The midpoint is the average of the two points, taken coordinate by coordinate. Averaging the x values gives the halfway x, averaging the y values gives the halfway y, and the result is equidistant from both ends by construction.
How to solve it by hand
- Add the two x values and halve the result
- Add the two y values and halve that too
- Pair them up as (x, y)
- Check: the distance to each end should be the same
What is worth knowing
The averaging idea generalises further than it first appears. Weighting the average moves the point along the segment: a 1:2 weighting lands a third of the way along, which is how you divide a segment in any ratio. Averaging three points gives the centroid of a triangle, the point where its medians meet and where it balances. And the same construction in three dimensions works unchanged. The midpoint also gives you the perpendicular bisector for free — the line through it at right angles to the segment, which is the set of all points equidistant from both ends.