What does the midpoint formula calculate?

The midpoint formula is designed to find a point that divides a segment into two equal parts, or congruent segments. This is especially useful in geometry when dealing with line segments in a coordinate plane. The formula is given by the coordinates of the midpoint, calculated as:

Midpoint (M) = ( \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) )

Here, ( (x_1, y_1) ) and ( (x_2, y_2) ) are the coordinates of the endpoints of the line segment. By averaging the x-coordinates and the y-coordinates of the two endpoints, the formula determines the location of the midpoint, ensuring that it is equidistant from both endpoints. This makes it a crucial tool for various applications in geometry, such as bisecting segments in constructions or locating centers within shapes.

In contrast, the other options pertain to different geometric concepts. The length of a segment requires the distance formula, the slope involves calculating the rise over run between two points, and the origin refers to the point ( (0,0) ) in the coordinate system. Thus