Length of the line segment that is perpendicular to these two lines and connects them.

### Example

Consider the parallel lines \(d_1\) and \(d_2\) :

Therefore: d(\(d_1\), \(d_2\)) = 2

In the Cartesian plane, if \(d_1\) has the equation “*y* = m*x* + b” and if \(d_2\) has the equation “*y* = m*x* + b'”, with b ≥ b’, then:

\(\textrm{m}\space\overline{\textrm{AB}}=\dfrac{\textrm{b}-\textrm{b’}}{\sqrt{\textrm{m}^2+1}}\).

Therefore, if \(d_1\) has the equation “*y* = 3*x* + 8″ and if \(d_2\) has the equation “*y* = 3*x* + 4″, then:

\(\textrm{m}\space\overline{\textrm{AB}}=\dfrac{\textrm{8}-\textrm{4}}{\sqrt{\textrm{3}^2+1}}\).