Distance Calculator — Calculadora Online Grátis
2D distance between two coordinates with midpoint, slope and line equation
The Distance Calculator computes the Euclidean distance between two points in 2D coordinate space, along with the midpoint coordinates, the slope of the connecting line, and the equation of that line in both slope-intercept and standard form. Geometry students, computer graphics programmers, and anyone working with Cartesian coordinates use this as a quick analytical geometry tool.
Frequently Asked Questions
Sobre Esta Calculadora
The distance between two points (x₁, y₁) and (x₂, y₂) in the Cartesian plane is given by the distance formula d = √((x₂−x₁)² + (y₂−y₁)²), which is a direct application of the Pythagorean theorem in two dimensions. The horizontal and vertical separations form the two legs, and the distance is the hypotenuse.
Beyond the distance, this calculator provides the midpoint (the point equidistant from both endpoints), the slope of the connecting line (rise over run), and the line equation in slope-intercept form (y = mx + b). These four quantities are the building blocks of coordinate geometry.
Applications include game development (collision detection, pathfinding), computer graphics (rendering distances), GPS navigation (approximating short-distance paths as flat), robotics (planning arm movements), and geometry coursework at the high school and college level.
The Distance Calculator computes the Euclidean distance between two points in 2D coordinate space, along with the midpoint coordinates, the slope of the connecting line, and the equation of that line in both slope-intercept and standard form. Geometry students, computer graphics programmers, and anyone working with Cartesian coordinates use this as a quick analytical geometry tool.
Exemplo Resolvido
Distance, midpoint and line equation between (1, 2) and (7, 10)
Entradas:
- Point 1: (1, 2)
- Point 2: (7, 10)
Passo a Passo:
- Distance formula: d = √((x₂−x₁)² + (y₂−y₁)²)
- d = √((7−1)² + (10−2)²) = √(6² + 8²) = √(36 + 64) = √100 = 10
- Midpoint: ((x₁+x₂)/2, (y₁+y₂)/2) = ((1+7)/2, (2+10)/2) = (4, 6)
- Slope: m = (y₂−y₁)/(x₂−x₁) = (10−2)/(7−1) = 8/6 = 4/3
- Line equation (point-slope): y−2 = (4/3)(x−1)
- Slope-intercept form: y = (4/3)x + 2/3