# Distance Between Two Parallel Lines

## Distance Between Two Parallel Lines

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:

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