How do you calculate the distance between two points?

The distance between two points in a Cartesian coordinate system can be accurately calculated using the distance formula. This formula is derived from the Pythagorean theorem, which relates the sides of a right triangle. When determining the distance between two points, (x1, y1) and (x2, y2), the distance formula is expressed as:

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

This calculation effectively allows you to find the straight-line distance between the two points by treating the differences in the x-coordinates and y-coordinates as the two legs of a right triangle, with the distance as the hypotenuse.

While the Pythagorean theorem lays the groundwork for this concept, the distance formula specifically provides a direct method for computing the distance between two points, making it the most appropriate choice. The midpoint formula calculates the midpoint between two points, and the slope formula determines the steepness of a line between two points, neither of which directly address the calculation of distance.