Definition: The midpoint of a segment is the point exactly halfway between its endpoints, dividing the segment into two congruent parts.
What is a midpoint?
If M is the midpoint of segment AB, then AM = MB = half of AB. A segment has exactly one midpoint.
What is the midpoint formula?
For endpoints (x1, y1) and (x2, y2), the midpoint is ((x1 + x2)/2, (y1 + y2)/2). You are averaging the coordinates.
Example. Find the midpoint of A(-7, 4) and B(5, -10). The x-coordinate is (-7 + 5)/2 = -1. The y-coordinate is (4 + (-10))/2 = -3. The midpoint is (-1, -3). You can also run it backward: if M(2, 6) is the midpoint and one endpoint is (-3, 1), the other endpoint has x = 2(2) – (-3) = 7 and y = 2(6) – 1 = 11, so it is (7, 11).
What errors show up?
Subtracting the coordinates instead of adding them, or dividing only one of the sums by 2. Subtracting finds a distance-like quantity, not a center. A midpoint is also a point, so give two coordinates in the answer.
Where to learn it
- Proving Shapes with Coordinates and Slopes – lesson
- Points, Segments and Angles: Core Definitions – lesson