Coordinate Geometry Calculator - Free Line Equations & Intersection Calculator
Coordinate Geometry Calculator
Calculate line equations, find intersections, and analyze geometric properties in the coordinate plane.
Find Line Equation
Enter two points to find the equation of the line
Point 1
Point 2
Results
Slope-Intercept Form
Standard Form
Slope (m)
Y-Intercept
X-Intercept
Intersection Point
Angle Between Lines
New Slope
Relationship
How to use this calculator
📊 How to Use the Coordinate Geometry Calculator
- Choose a calculation type: Line Equation, Intersection, or Parallel/Perpendicular
- For Line Equation: Enter two points to find the equation
- For Intersection: Enter coefficients of two lines in standard form
- For Parallel/Perpendicular: Enter original line and a point
- View the graph and all calculated properties
📐 Line Equation Forms
Slope-Intercept Form
y = mx + b
Where m is slope and b is y-intercept
Standard Form
ax + by = c
Where a, b, and c are constants
Point-Slope Form
y - y₁ = m(x - x₁)
Where m is slope and (x₁, y₁) is a point
🌟 Key Concepts
Slope Formula
m = (y₂ - y₁) / (x₂ - x₁)
Parallel Lines
Have the same slope: m₁ = m₂
Perpendicular Lines
Slopes multiply to -1: m₁ × m₂ = -1
Distance from Point to Line
d = |ax₀ + by₀ + c| / √(a² + b²)
💡 Pro Tips
- • Vertical lines have undefined slope and equation x = k
- • Horizontal lines have slope 0 and equation y = k
- • To check if a point is on a line, substitute its coordinates
- • The angle between two lines can be found using their slopes
- • Standard form is useful for finding intercepts quickly
- • Slope-intercept form is best for graphing
⚠️ Common Mistakes to Avoid
- • Remember slope is rise over run, not run over rise
- • Be careful with negative slopes - they go down from left to right
- • Don't divide by zero when finding slope of vertical lines
- • Perpendicular to a horizontal line is vertical (not zero slope)
- • Check your signs when converting between equation forms
About this calculator
Calculate line equations, find intersections, perpendicular and parallel lines, and analyze geometric properties in the coordinate plane.
Was this helpful?
Browse more in
Related Calculators
Triangle Area Calculator - Free Online Geometry Calculator
Calculate triangle area using multiple methods: base-height, three sides (Heron's formula), or coordinates. Perfect for students and educators.
Circle Calculator - Free Online Circle Area & Circumference Calculator
Calculate circle area, circumference, diameter, and radius instantly. Free online circle calculator with visual diagram and step-by-step solutions.
Rectangle & Square Calculator - Free Online Area, Perimeter & Diagonal Calculator
Calculate rectangle and square area, perimeter, and diagonal length instantly. Free online calculator with visual diagrams and step-by-step solutions.
Pythagorean Theorem Calculator - Free Online Right Triangle Calculator
Calculate missing sides of right triangles using the Pythagorean theorem. Find hypotenuse or legs with our free visual calculator and step-by-step solutions.
Polygon Area Calculator - Free Online Regular Polygon Calculator
Calculate area and perimeter of regular polygons (pentagon, hexagon, octagon, etc.). Free calculator with visual diagrams and formulas.
3D Volume Calculator - Free Online Cube, Sphere, Cylinder & Cone Calculator
Calculate volume and surface area of 3D shapes including cubes, spheres, cylinders, cones, and pyramids. Free calculator with visual diagrams.