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Perpendicular Line Through a Point Calculator — result sheet
Build the equation of a line perpendicular to a nonhorizontal reference slope through a chosen point.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: Perpendicular slope m⊥=−1/m; b=y₀−m⊥x₀.
For finite nonzero slopes, perpendicular lines use negative reciprocal slopes; the supplied point determines the intercept.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Reference slope — minimum -1000000000000; maximum 1000000000000
- Point x — minimum -1000000000000; maximum 1000000000000
- Point y — minimum -1000000000000; maximum 1000000000000
Worked example
| Input | Value |
|---|---|
| Reference slope | 2 |
| Point x | 3 |
| Point y | 4 |
Perpendicular slope =−0.5; y=−0.5x+5.5.
Assumptions and limits
- The reference slope is nonzero and finite.
- Both lines are represented in Cartesian slope-intercept form.
- Horizontal and vertical special cases are not modeled by this contract.
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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