What is the midpoint formula between two points (x1, y1) and (x2, y2)?

The midpoint formula is used to find the point that is exactly halfway between two given points in a Cartesian coordinate system. This is particularly useful in various applications such as geometry, computer graphics, and even real-life situations like finding the center point between two locations.

To derive the formula, consider two points: (x1, y1) and (x2, y2). To find the midpoint, you essentially need to average the x-coordinates and the y-coordinates of these two points.

The x-coordinate of the midpoint is calculated as the average of the x-coordinates: ((x1 + x2)/2). Similarly, the y-coordinate of the midpoint is calculated as the average of the y-coordinates: ((y1 + y2)/2).

Combining these two results gives us the complete midpoint formula:

[ M = \left( \frac{x1 + x2}{2}, \frac{y1 + y2}{2} \right) ]

This correctly captures the notion of finding the exact midpoint between the two points. Thus, the answer is correct because it accurately represents the mathematical principle behind calculating a midpoint in a two-dimensional space.