# Condition for Straight Lines in Plane to be Perpendicular

## 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:

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