Distance Formula Calculator
Calculate the distance between two points using the distance formula with detailed step-by-step solutions and midpoint calculation.
Enter Coordinates
Point A (x₁, y₁)
Point B (x₂, y₂)
Results
Enter coordinates for both points to calculate distance
Distance Formula
d = √[(x₂ - x₁)² + (y₂ - y₁)²]
Where (x₁, y₁) and (x₂, y₂) are the coordinates of the two points
How It Works
Pythagorean Connection
The distance formula comes from the Pythagorean theorem:
Horizontal distance: |x₂ - x₁|
Vertical distance: |y₂ - y₁|
Hypotenuse: √[(x₂-x₁)² + (y₂-y₁)²]
Midpoint Formula
The midpoint is the average of coordinates:
M = ((x₁ + x₂)/2, (y₁ + y₂)/2)
It's the point exactly halfway between the two points.
Examples
Example 1: Simple Integer Points
Points: A(0, 0) and B(3, 4)
Distance: √[(3-0)² + (4-0)²] = √[9 + 16] = √25 = 5
Midpoint: ((0+3)/2, (0+4)/2) = (1.5, 2)
Example 2: Negative Coordinates
Points: A(-2, -1) and B(1, 3)
Distance: √[(1-(-2))² + (3-(-1))²] = √[9 + 16] = 5
Midpoint: ((-2+1)/2, (-1+3)/2) = (-0.5, 1)
Applications
Geometry
Finding lengths of sides in triangles, diagonals in rectangles, and distances in coordinate geometry problems.
Physics
Calculating displacement, finding distances between objects, and analyzing motion in 2D space.
Computer Graphics
Collision detection, pathfinding algorithms, and calculating distances between pixels or objects.
Navigation
GPS systems, mapping applications, and calculating straight-line distances between locations.
Frequently Asked Questions
The distance formula calculates the straight-line distance between two points in a coordinate plane: d = √[(x₂ - x₁)² + (y₂ - y₁)²]. It's derived from the Pythagorean theorem.