Find the distance between two points using the distance formula, with steps and diagram.
Calculate distances on a Cartesian plane with visual representation
Enter Coordinates
Coordinate System
2D Cartesian Plane
Results
Distance Formula
d = √((x₂ - x₁)² + (y₂ - y₁)²)
Step-by-Step Calculation
Final Answer
Distance = 0 units
Enter coordinates and click "Calculate Distance" to see results
Coordinate Plane Diagram
XY Plane
XZ Plane
About the Distance Formula
The distance between two points in a plane can be found using the Pythagorean theorem, expressed as the distance formula. This formula calculates the straight-line distance between two points in a Cartesian coordinate system.
Examples:
- Horizontal line: For points (2, 3) and (7, 3), distance = |7 - 2| = 5 units
- Vertical line: For points (4, 1) and (4, 8), distance = |8 - 1| = 7 units
- Diagonal line: For points (1, 1) and (4, 5), distance = √((4-1)² + (5-1)²) = 5 units
- 3D space: For points (1, 2, 3) and (4, 6, 9), distance = √((4-1)² + (6-2)² + (9-3)²) = √(9+16+36) = √61 ≈ 7.81 units
Real-World Applications:
The distance formula is used in navigation, physics, map-making, computer graphics, and many other fields. It helps calculate the shortest path between two points, which is essential in GPS technology, robotics, and game development.
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