Distance Formula
The distance between two points (x₁, y₁) and (x₂, y₂) in a coordinate plane is derived from the Pythagorean theorem.
d = √[(x₂−x₁)² + (y₂−y₁)²]
Example: (1,2) to (4,6): d = √[(4−1)²+(6−2)²] = √(9+16) = √25 = 5
Example: (1,2) to (4,6): d = √[(4−1)²+(6−2)²] = √(9+16) = √25 = 5
Applications
- Finding the length of a line segment on a graph
- Computer graphics and game development
- Mapping and navigation systems
- Geometry and coordinate geometry problems