Equation of a Line

307. The Perpendicular Product · when slopes multiply to –1

The product of the slopes of two perpendicular lines is always –1.

OBCDα = 27°α = 27°θ = 117°θ = 117°m₁ = tan α = 0.5m₁ = tan α = 0.5m₂ = tan θ = -2m₂ = tan θ = -2m₁ · m₂ = -1m₁ · m₂ = -1A
Perpendicular lines have slopes whose product is −1: m₁ × m₂ = −1, so each slope is the negative reciprocal of the other (the vertical–horizontal pair being the special case).
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