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Points formulas
11 formulas for Points, from the Coordinate Geometry section of the Quantix formula library. Tap 🧮 next to a formula to solve it for any variable with step-by-step working.
| Name | Formula | Note |
|---|---|---|
| Distance | d = √((x₂ − x₁)² + (y₂ − y₁)²) 🧮 Solve step by step | |
| Distance from origin | √(x² + y²) | |
| Mid-point | ((x₁ + x₂)/2, (y₁ + y₂)/2) | |
| Section — internal m : n | ((mx₂ + nx₁)/(m + n), (my₂ + ny₁)/(m + n)) | |
| Section — external m : n | ((mx₂ − nx₁)/(m − n), (my₂ − ny₁)/(m − n)) | |
| Centroid | ((x₁ + x₂ + x₃)/3, (y₁ + y₂ + y₃)/3) | |
| Incentre | ((ax₁ + bx₂ + cx₃)/(a + b + c), (ay₁ + by₂ + cy₃)/(a + b + c)) | |
| Triangle area | ½ |x₁(y₂ − y₃) + x₂(y₃ − y₁) + x₃(y₁ − y₂)| | |
| Collinear points | triangle area = 0 | |
| Polygon area (shoelace) | ½ |Σ (xᵢyᵢ₊₁ − xᵢ₊₁yᵢ)| | |
| Polar ↔ Cartesian | x = r cos θ, y = r sin θ; r = √(x² + y²), θ = tan⁻¹(y/x) 🧮 Solve step by step |
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