What is the midpoint formula used to find?

The midpoint formula is used to find the average coordinates of two points in a Cartesian coordinate system. Specifically, if you have two points with coordinates ((x_1, y_1)) and ((x_2, y_2)), the midpoint, M, can be calculated using the formula:

[

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

]

This formula effectively averages the x-coordinates and the y-coordinates of the two points, resulting in a new point that is exactly halfway between them.

Understanding the midpoint is useful in various applications, such as geometry and coordinate systems, because it allows one to easily find a central location between two distinct points. It is not concerned with the maximum distance, the slope of the line, or the angle between lines, which are addressed by different methods and formulas.