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Perpendicular lines meet slopes m and −1/m. Enter the original slope and a point; horizontal originals correctly yield vertical lines (x = constant) instead of an error.
Negative-reciprocal slope through your point; verticals handled.
m′ = −1/m through (x₀, y₀); m = 0 → x = x₀
| Symbol | Meaning |
|---|---|
| m′ | New slope, the negative reciprocal |
| (x₀,y₀) | Point on the new line |
Perpendicular to slope 2 through (1,1): m′ = −0.5, b = 1.5 → y = −0.5x + 1.5.
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Rotating a direction 90° negates and inverts the rise/run ratio — equivalently, m₁·m₂ = −1.
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Content updated: September 2026