The Midpoint of a Segment

The midpoint of a line segment is the point exactly halfway between its two ends. To find it you don't need to measure — you just average the coordinates: take the average of the two x-values and the average of the two y-values.

So the midpoint of the segment from (x_1, y_1) to (x_2, y_2) is

\left(\tfrac{x_1+x_2}{2},\ \tfrac{y_1+y_2}{2}\right)

For a segment from (x_1, y_1) to (x_2, y_2):

the midpoint is \left(\tfrac{x_1+x_2}{2},\ \tfrac{y_1+y_2}{2}\right) — average the x's, average the y's;
it lies exactly halfway along the segment, splitting it into two equal halves.

See the averaging

Step through the figure. The midpoint M lands at the average of the endpoints' coordinates, so it sits right in the middle of the segment.