What is the midpoint formula for two points?

The midpoint formula for two points in a Cartesian coordinate system is derived from the concept of finding the average of the x-coordinates and the average of the y-coordinates of the two given points. If you have two points, (x₁, y₁) and (x₂, y₂), the midpoint is calculated by taking the average of the x-coordinates and the average of the y-coordinates.

The formula is structured as follows: for the x-coordinate of the midpoint, you add x₁ and x₂ and then divide by 2, which gives you (x₁ + x₂)/2. Similarly, to find the y-coordinate of the midpoint, you add y₁ and y₂ and divide by 2, resulting in (y₁ + y₂)/2.

This results in the midpoint being expressed as:

Midpoint = ((x₁ + x₂)/2, (y₁ + y₂)/2)

This calculation provides the coordinates of the point that is exactly halfway between the two points on both the x and y axes, effectively giving you the centroid of the line segment connecting them. Thus, this formulation is essential in various applications, such as geometry, computer graphics, and