Perpendicular Lines — Cheat sheet

The condition

$m_1 \cdot m_2 = -1$, that is $m_2 = -\dfrac{1}{m_1}$ - the negative reciprocal. In standard form: $a_1a_2 + b_1b_2 = 0$.

Flipping slopes

Shortcut

Perpendicular to $ax + by + c = 0$ is $bx - ay + k = 0$: swap the coefficients, negate one, substitute the point for $k$.

Trap

Horizontal and vertical lines are perpendicular, but the product rule cannot show it - $0 \times$ undefined means nothing. Use the coefficient form.