# Distance between Two Parallel Lines

In order to find the distance between two parallel lines, first we find a point on one of the lines then we find its distance from the other line.
For example, consider the equations of parallel lines are given as

Let $\left( {{x_1},{y_1}} \right)$ be a point on the line (i), then its distance from the line (ii) will be the distance between the lines (i) and (ii).
Now the distance of the point $\left( {{x_1},{y_1}} \right)$ from the line (ii) is given by

Alternatively we can find distance between two parallel lines as
Considers two parallel lines

Now distance between two parallel lines by the following formula

Example: Find the distance between the parallel lines
$3x - 4y + 3 = 0\,\,\,{\text{ - - - }}\left( {\text{i}} \right)$ and $6x - 8y + 7 = 0\,\,\,{\text{ - - - }}\left( {{\text{ii}}} \right)$
Find we find a point $A$ on (i). For this, we put $y = 0$ in equation (i), i.e.

Thus, $A\left( { - 1,0} \right)$ is a point on line (i). If $d$ is the distance between given lines (i) and (ii), then $d$ is the distance of the point $A$ from the line (ii), so