Coordinate Geometry Calculator
Calculate distance between points, slope, midpoint, and equations of lines in the coordinate plane. These tools help solve problems in analytic geometry and understand the relationships between geometric figures and algebraic equations.
Results
Distance Between Points
Point 1: (2, 3)
Point 2: (5, 7)
Distance: 3.6056
Slope Calculation
Point 1: (1, 2)
Point 2: (3, 4)
Slope (m): 1
Interpretation: Positive slope (line rises from left to right)
Midpoint Calculation
Point 1: (-2, 4)
Point 2: (6, -4)
Midpoint: (2, 0)
Line Equation
Point 1: (0, 2)
Point 2: (2, 4)
Slope (m): 1
Y-intercept (b): 2
Equation: y = 1x + 2
About Coordinate Geometry
Coordinate geometry (or analytic geometry) is the study of geometry using a coordinate system. This combines algebra and geometry to describe the position of points, lines, and shapes. The Cartesian coordinate system is most commonly used, with points defined by their distance from two perpendicular axes (x and y).
Key Concepts
Coordinate geometry provides powerful tools to solve geometric problems algebraically:
Distance Between Two Points
The distance d between two points (x₁, y₁) and (x₂, y₂) is given by:
d = √[(x₂ - x₁)² + (y₂ - y₁)²]
Slope of a Line
The slope m of a line passing through points (x₁, y₁) and (x₂, y₂) is:
m = (y₂ - y₁) / (x₂ - x₁)
A positive slope indicates the line rises from left to right, while a negative slope indicates it falls. A zero slope means the line is horizontal, and an undefined slope means the line is vertical.
Midpoint of a Line Segment
The midpoint M between two points (x₁, y₁) and (x₂, y₂) is:
M = ((x₁ + x₂)/2, (y₁ + y₂)/2)
Equation of a Line
The slope-intercept form of a line's equation is:
y = mx + b
where m is the slope and b is the y-intercept (where the line crosses the y-axis).
Applications
Coordinate geometry has wide applications in mathematics, physics, engineering, computer graphics, and more. It's essential for:
- Graphing functions and relationships
- Solving systems of equations
- Analyzing geometric shapes and their properties
- Computer graphics and game development
- Navigation and GPS systems