🎓 Mathematics • Coordinate Geometry
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Coordinate Geometry Calculator
Computes Euclidean distance, midpoint coordinates, slope, inclination angle, and line equation between two points.
2D Coordinate Geometry: Points P₁ & P₂
Enter real (x, y) coordinates to calculate distance, midpoint, slope, angle, and line equation.
Point 1: P₁(x₁, y₁)
Point 2: P₂(x₂, y₂)
Try Example Line Segments:
2D Cartesian Plane PlotLine: y = 1.3333x + 5.6667Scale: 16px/unit
Euclidean Distance (d)
10
d = √[(Δx)² + (Δy)²] = √[6² + 8²]Midpoint (M)
(1, 7)
M = ((x₁ + x₂)/2, (y₁ + y₂)/2)Slope (m) & Inclination (θ)
m = 1.3333
Angle θ = 53.13° (0.9273 rad)Line Equation (Slope-Intercept)
y = 1.3333x + 5.6667
Standard: -1.3333x + 1y = 5.6667Detailed Mathematical Derivations:
1. Euclidean Distance Formula:
d = √[(x₂ - x₁)² + (y₂ - y₁)²]
= √[(4 - -2)² + (11 - 3)²]
= √[(6)² + (8)²] = √100
= 10 units
2. Midpoint Coordinates:
M = ((x₁ + x₂) / 2, (y₁ + y₂) / 2)
= ((-2 + 4) / 2, (3 + 11) / 2)
= (1, 7)
3. Slope & Rate of Change:
m = (y₂ - y₁) / (x₂ - x₁) = Δy / Δx
= (11 - 3) / (4 - -2) = 8 / 6
= 1.3333
4. Equations of the Line:
• Point-Slope: y - (3) = 1.3333(x - (-2))
• Slope-Intercept: y = 1.3333x + 5.6667
• General Standard: -1.3333x + 1y = 5.6667
What is Coordinate Geometry?
Coordinate geometry (analytic geometry) studies geometry using a coordinate Cartesian plane.
It links algebraic equations with geometric straight lines and curves.
Formula & Step-by-Step Calculation
d = √[(x₂ - x₁)² + (y₂ - y₁)²], m = (y₂ - y₁) / (x₂ - x₁)
Euclidean distance and slope formulas.
Worked Step-by-Step Examples
Example 1
Distance between (0, 0) and (3, 4)
Solution: 5
• d = √[3² + 4²] = √25 = 5
Common Real-World & Academic Use Cases
- ✓ GPS navigation distances
- ✓ Computer graphics 2D line drawing algorithms
- ✓ Surveying slope grade calculation
How to Use the Coordinate Geometry Calculator
1
Enter Point 1 (x₁, y₁)
Input first coordinate.
2
Enter Point 2 (x₂, y₂)
Input second coordinate.
3
Review Results
Inspect distance, midpoint, slope, and line equation.
Frequently Asked Questions
Q: What is the slope of a vertical line?
Undefined, because Δx = 0 causing division by zero.