Calculate the distance between two points on a coordinate plane
The distance formula calculates the straight-line distance between two points on a coordinate plane. It's derived from the Pythagorean theorem, where the horizontal and vertical distances form the legs of a right triangle, and the distance between the points is the hypotenuse.
Where (x₁, y₁) and (x₂, y₂) are the coordinates of the two points
The midpoint is the point exactly halfway between the two points
Calculate distances between locations on maps and coordinate systems for routing and navigation.
Determine distances between pixels, objects, and points in 2D and 3D rendering.
Calculate displacement, trajectory paths, and spatial relationships in physical systems.
Measure distances between game objects for collision detection and AI pathfinding.
The distance formula is a direct application of the Pythagorean theorem (a² + b² = c²), where the horizontal distance is one leg, the vertical distance is the other leg, and the distance between points is the hypotenuse.
The distance formula calculates Euclidean distance, which is the shortest straight-line distance between two points. This is the most common distance metric in mathematics and physics.
The distance from point A to point B is the same as the distance from point B to point A. You can label either point as (x₁, y₁) and get the same result.
The distance formula extends to three dimensions: d = √[(x₂-x₁)² + (y₂-y₁)² + (z₂-z₁)²], adding the z-coordinate difference.
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