Distance formula

The distance formula gives the straight-line distance between two points from their coordinates, using the Pythagorean theorem.

Pythagorean theorem: A theorem stating that a right triangle’s hypotenuse squared equals the sum of its legs squared. The distance formula applies this theorem to horizontal and vertical coordinate differences.
Cartesian coordinate system: A system that locates points using signed distances along perpendicular axes. The formula uses coordinates measured along perpendicular Cartesian axes.
Midpoint formula: A formula that finds the point halfway between two endpoints of a line segment. Distance and midpoint formulas use the same pair of endpoint coordinates.
Manhattan distance: A distance measure that sums absolute coordinate differences along axis-aligned paths. Unlike straight-line distance, it restricts movement to coordinate directions.
Euclidean distance: The ordinary straight-line distance between points in Euclidean space. The formula computes Euclidean distance from coordinates in the plane.
Ordered pair: A pair of numbers whose order distinguishes the first entry from the second. Each plane point is written as an ordered pair of coordinates.
Circle: The set of points in a plane at a fixed distance from a center. The distance formula tests whether a point lies at a circle’s radius from its center.
Chebyshev distance: A distance measure equal to the largest absolute coordinate difference. It measures maximum axis displacement rather than the diagonal length.
Coordinate plane: A plane where each point is identified by an ordered pair of numbers. The formula measures separation between points represented on this plane.
Absolute value: The nonnegative magnitude of a real number, regardless of its sign. Coordinate differences may be negative, but their squared contributions are nonnegative.

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