In coordinate geometry, how is the distance between two points calculated?

The distance between two points in coordinate geometry is determined using the Distance Formula, which is derived from the Pythagorean theorem. When you have two points, denoted as (x₁, y₁) and (x₂, y₂), the formula for calculating the distance between them is given by:

Distance = √((x₂ - x₁)² + (y₂ - y₁)²).

This formula calculates the straight-line distance between the two points in a two-dimensional plane. It considers the horizontal and vertical distances between the points by taking the difference of the x-coordinates (x₂ - x₁) and the y-coordinates (y₂ - y₁), then applying the Pythagorean theorem, which involves squaring each of these differences, summing them up, and taking the square root of the result.

This approach is accurate because it accounts for both dimensions in a geometric way, ensuring that the resulting distance reflects the actual straight-line measurement between the two points. The other options do not correctly represent this relationship, either by adding or misapplying the differences or using incorrect arithmetic.