What Is the Midpoint Theorem?

The midpoint theorem is a theory used in coordinate geometry that states that the midpoint of a line segment is the average of its endpoints. Solving an equation using this method requires that both the x and y coordinates are known. This theorem can also be used in algebra and calculus.

A line segment is defined by two endpoints on a coordinate axis. These endpoints have x and y values on the coordinate plane. The midpoint theorem takes the average of the x coordinates and the average of the y coordinates to produce the midpoint of the line segment. For example, a line segment with the endpoints of (6,4) and (2,2) is calculated as follows: (6+2)/2 = 4, (4+2)/2 = 3. Therefore, the midpoint of this segment is located at (4,3). This theorem can also be used to find a unknown endpoint, provided that the midpoint and one endpoint are already known.

This theorem can be proved using triangles. For a line segment that is on an angle, if two lines are drawn parallel to the x-axis and y-axis that begin at the endpoints and the midpoint, the result is two similar triangles. The relation of these triangles produces the midpoint theorem.