What does the distance formula calculate between two points (x₁, y₁) and (x₂, y₂)?

The distance formula calculates the straight-line distance between two points in a two-dimensional Cartesian coordinate system. The formula is derived from the Pythagorean theorem, which relates the lengths of the sides of a right triangle to the lengths of its hypotenuse.

Given two points (x₁, y₁) and (x₂, y₂), the change in the x-coordinates is (x₂ - x₁), and the change in the y-coordinates is (y₂ - y₁). These changes effectively create the lengths of the two legs of a right triangle where the hypotenuse represents the distance between the two points.

By applying the Pythagorean theorem, the distance ( d ) is computed using the formula:

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

This method captures the true straight-line distance between the two points in the coordinate plane, incorporating both the horizontal and vertical differences.

This approach accurately reflects how distance is calculated in a two-dimensional space, making option B the correct answer.