How is the midpoint of a line segment represented mathematically?

The midpoint of a line segment is the point that is exactly halfway between the endpoints of that segment. Mathematically, this is achieved by taking the average of the x-coordinates and the average of the y-coordinates of the endpoints.

Given two endpoints of a line segment, labeled as (x₁, y₁) and (x₂, y₂), the calculation for the midpoint involves adding the x-coordinates together and dividing by 2, followed by adding the y-coordinates together and dividing by 2. This means that the x-coordinate of the midpoint is (x₁ + x₂)/2 and the y-coordinate is (y₁ + y₂)/2. Therefore, the correct mathematical representation of the midpoint is ((x₁ + x₂)/2, (y₁ + y₂)/2).

This representation effectively ensures that the midpoint lies equidistant from both endpoints in both the horizontal and vertical directions, which is essential for it to be the true midpoint of the segment.