What is the formula for the midpoint in a two-dimensional coordinate system?

The formula for the midpoint in a two-dimensional coordinate system is derived from the need to find the average position between two points, represented by their coordinates (x₁, y₁) and (x₂, y₂). The midpoint's x-coordinate is found by taking the average of the x-coordinates of the two points, which is calculated as (x₁ + x₂)/2. Similarly, the y-coordinate of the midpoint is obtained by averaging the y-coordinates, yielding (y₁ + y₂)/2.

Thus, the complete formula for the midpoint is expressed as ((x₁ + x₂)/2, (y₁ + y₂)/2). This correctly reflects the geometry of finding a point that is equidistant from both of the original points in both the x and y directions.

In contrast, the other formulas fail to accurately calculate the midpoint. They either involve incorrect operations like subtraction or multiplication, or do not properly average the coordinates, which are essential in determining the true midpoint location.