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 = mx + b” and if \(d_2\) has the equation “y = mx + 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 = 3x + 8″ and if \(d_2\) has the equation “y = 3x + 4″, then:
\(\textrm{m}\space\overline{\textrm{AB}}=\dfrac{\textrm{8}-\textrm{4}}{\sqrt{\textrm{3}^2+1}}\).