a midpoint
Fold a strip of paper end to end and the crease lands exactly halfway: it splits the strip into two equal pieces. That halfway point of a segment is its midpoint.
Precisely, the midpoint of a segment AB is the point M that lies on AB and is equidistant from the two ends, so that AM = MB. Because M is between A and B and the two halves are equal, each half is exactly half the whole: AM = MB = (1/2)·AB. On a number line the midpoint's coordinate is simply the average of the endpoints' coordinates, (a + b)/2; in the coordinate plane the midpoint of the segment from (x_1, y_1) to (x_2, y_2) is ((x_1 + x_2)/2, (y_1 + y_2)/2). A segment has exactly one midpoint.
The midpoint is one of the most-used special points in geometry. It is where you bisect a segment, the centre of a circle drawn on a segment as diameter, and the meeting place of a triangle's medians (each median runs from a vertex to the midpoint of the opposite side). Take care to separate the midpoint from the perpendicular bisector: the midpoint is a single point on the segment, while the perpendicular bisector is the whole line through that midpoint at right angles to the segment — the set of all points equidistant from A and B.
The midpoint of the segment from A(2, 3) to B(8, 11) is ((2 + 8)/2, (3 + 11)/2) = (5, 7). On a plain number line, the midpoint of the points at 4 and 10 is at (4 + 10)/2 = 7, equidistant from both.
A midpoint is the single halfway point: average the coordinates.
The midpoint is one point on the segment; the perpendicular bisector is the whole line through it at right angles — don't conflate the point with the line.