What does "distance between two points" refer to in mathematics?

The term "distance between two points" in mathematics refers to the absolute difference in their coordinates. This concept is especially applicable in the context of a coordinate system, where each point is defined by its coordinates, such as (x₁, y₁) and (x₂, y₂).

To calculate the distance between two points in a one-dimensional space, simply taking the absolute difference between their coordinates provides the length between those two points. In two-dimensional space, the distance is typically calculated using the distance formula, which incorporates both the differences in x and y coordinates. However, the foundational idea remains that it is based on the absolute difference of their positions, making this concept critical for understanding geometric relationships on a graph.

The other options present different operations that do not accurately describe the concept of distance in mathematics. The sum or product of coordinates, or the average of coordinates, does not equate to the actual physical distance between points. Hence, the absolute difference is the correct way to encapsulate what the distance between two points represents.