Question

Write the distance between the lines 4x + 3y − 11 = 0 and 8x + 6y − 15 = 0.

Answer 1

The distance between the two parallel lines $ax+by+c_1=0\mathrm{and}ax+by+c_2=0$ is $\left|\frac{c_1-c_2}{\sqrt{a^2+b^2}}\right|$.
The given lines can be written as

4x + 3y − 11 = 0 ... (1)

$8x+6y-15=0\Rightarrow 4x+3y-\frac{15}{2}=0$ ... (2)

Let d be the distance between the lines (1) and (2).

$d=\left|\frac{-11-\left(-{\displaystyle \frac{15}{2}}\right)}{\sqrt{4^2+3^2}}\right|=\frac{7}{10}$ units