Final answer:
The distance formula is used to calculate the distance between two points in space, extending the Pythagorean theorem to Cartesian coordinates in two or three dimensions.
Step-by-step explanation:
The distance formula on a coordinate plane is used to calculate the distance between two points in Euclidean space. When dealing with Cartesian coordinates, the distance can be determined by using the Pythagorean theorem. For two points (x1, y1) and (x2, y2), the distance (d) between these points is given by:
d = √((x2 - x1)² + (y2 - y1)²)
In a three-dimensional space, this formula extends to account for the z-coordinate as well:
d = √((x2 - x1)² + (y2 - y1)² + (z2 - z1)²)
Here, d represents the linear distance between the two points, and √ symbolizes the square root. The formula essentially calculates the length of the hypotenuse of a right-angled triangle formed by the points when plotted on a graph, thus applying the Pythagorean theorem.