How is the length of a line segment calculated between two points?

The length of a line segment between two points in a coordinate plane is determined using the distance formula, which is derived from the Pythagorean theorem. If you have two points, represented as (x1, y1) and (x2, y2), the distance between these points can be calculated as the square root of the sum of the squares of the differences in their coordinates.

By taking the differences of the x-coordinates and y-coordinates—specifically, (x1 - x2) and (y1 - y2)—and then squaring these differences, you effectively create a right triangle where these differences represent the legs. The length of the hypotenuse, which is the distance between the two points, is found by applying the square root to the sum of these squared differences:

[ d = \sqrt{(x1 - x2)^2 + (y1 - y2)^2} ]

This formula precisely calculates the straight-line distance between two points in a two-dimensional space, making it indispensable in geometry and various applications of mathematics. Therefore, the choice that represents this calculation accurately is the correct answer.