Coordinate Geometry Calculator (Distance, Midpoint, Slope)
🎯 Select Calculation Type:
📊 Enter Point Coordinates:
Point A (x₁, y₁):
Point B (x₂, y₂):
📊 Visual Representation:
📍 Coordinate Geometry Calculator
Quickly calculate essential coordinate geometry parameters: distance between two points, midpoint coordinates of a line segment, and slope of a line. Perfect for solving analytical geometry problems.
🔍 Available Calculations:
- Distance between points - using Euclidean formula
- Midpoint of segment - coordinates of the center point
- Line slope - slope coefficient and angle of inclination
📝 Formulas:
Distance between points:
d = √[(x₂ - x₁)² + (y₂ - y₁)²]
Midpoint of segment:
M = ((x₁ + x₂)/2, (y₁ + y₂)/2)
Slope of line:
m = (y₂ - y₁)/(x₂ - x₁)
θ = arctan(m) × 180°/π
💡 Applications:
- Solving geometric problems
- Graphing functions
- Navigation and cartography
- Computer graphics
- Engineering calculations
- Physics motion problems
Frequently Asked Questions
What is the distance formula?
The distance formula d = √[(x₂-x₁)² + (y₂-y₁)²] is an application of the Pythagorean theorem to find the distance between two points on a coordinate plane.
How do I find the midpoint of a segment?
Midpoint coordinates are calculated as the arithmetic mean of corresponding coordinates of the endpoints: M((x₁+x₂)/2, (y₁+y₂)/2).
What does the slope of a line represent?
Slope (gradient) shows how much y changes when x changes by 1 unit. Positive slope means the line goes up, negative slope means it goes down.
When is the slope of a line undefined?
Slope is undefined when the line is vertical (x₁ = x₂), because this results in division by zero.
What is the relationship between slope and angle?
The angle of inclination θ is related to slope m by θ = arctan(m). A slope of 1 corresponds to a 45° angle.