Condition for Straight Lines in Plane to be Perpendicular

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Theorem

General Equation

Let $L_1$ and $L_2$ be straight lines embedded in a cartesian plane, given in general form:

\(\ds L_1: \, \) \(\ds l_1 x + m_1 y + n_1\) \(=\) \(\ds 0\)
\(\ds L_2: \, \) \(\ds l_2 x + m_2 y + n_2\) \(=\) \(\ds 0\)

Then $L_1$ is perpendicular to $L_2$ if and only if:

$l_1 l_2 + m_1 m_2 = 0$


Slope Form

Let $L_1$ and $L_2$ be straight lines in the Cartesian plane.

Let the slope of $L_1$ and $L_2$ be $\mu_1$ and $\mu_2$ respectively.


Then $L_1$ is perpendicular to $L_2$ if and only if:

$\mu_1 = -\dfrac 1 {\mu_2}$