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Line Equation From Two Points — result sheet
Construct a normalized A*x+B*y+C=0 line from two distinct two-dimensional Cartesian points, including vertical lines.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: Use raw coefficients A=y1-y2, B=x2-x1, C=x1*y2-x2*y1, then divide all three by sqrt(A^2+B^2) and choose a positive-first normal sign.
Two distinct points determine one line. The returned coefficients have unit normal length sqrt(A^2+B^2)=1 and satisfy A*x+B*y+C=0 for both points, with vertical lines represented directly rather than through an undefined slope.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Point 1 x — coordinate units; The x-coordinate of the first point.; minimum -1000000; maximum 1000000
- Point 1 y — coordinate units; The y-coordinate of the first point.; minimum -1000000; maximum 1000000
- Point 2 x — coordinate units; The x-coordinate of the second point.; minimum -1000000; maximum 1000000
- Point 2 y — coordinate units; The y-coordinate of the second point.; minimum -1000000; maximum 1000000
Worked example
| Input | Value |
|---|---|
| Point 1 x | 0 |
| Point 1 y | 0 |
| Point 2 x | 2 |
| Point 2 y | 2 |
The normalized coefficients are A=0.7071067812, B=-0.7071067812, C=0, giving 0.7071067812*x-0.7071067812*y=0, equivalent to x-y=0.
Assumptions and limits
- Both points use one flat two-dimensional Cartesian coordinate system and compatible coordinate units.
- The points are exact finite inputs for this calculation; no best-fit line, uncertainty model, or outlier handling is performed.
- Normalization means unit normal length plus a deterministic sign in which the first nonzero normal coefficient is positive.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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