In coordinate geometry, which formula is used to find the distance between two points?

The distance between two points in a coordinate plane is determined using the Distance Formula, which is derived from the Pythagorean theorem. This formula states that if you have two points, (x₁, y₁) and (x₂, y₂), the distance ( d ) between these points can be calculated using the expression:

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

This formula effectively squares the differences in x-coordinates and y-coordinates, adds those squared values together, and takes the square root. This process reflects the geometric relationship of a right triangle formed by the horizontal and vertical distances between the points.

Using this formula allows for calculating the straight-line distance, or Euclidean distance, between two points, which is fundamental in geometry and various applications in mathematics and real-world scenarios, such as navigation or computer graphics.