Question
Write the distance between the lines $4x + 3y - 11 = 0$ and $8x + 6y - 15 = 0$.
✓
Answer
The distance between the two parallel lines $a x+b y+c_1=0$ and $a x+b y+c_2=0$ is $\left|\frac{c_1-c_2}{\sqrt{a^2+b^2}}\right|$
The given lines can be written as
$4 x+3 y-11=0 \ldots(1)$
$8 x+6 y-15=0 \Rightarrow 4 x+3 y-\frac{15}{2}=0 \ldots(2)$
Let $d$ be the distance between the lines (1) and (2)
$d=\left|\frac{-11-\left(-\frac{15}{2}\right)}{\sqrt{4^2+3^2}}\right|=\frac{7}{10} \text { units }$
The given lines can be written as
$4 x+3 y-11=0 \ldots(1)$
$8 x+6 y-15=0 \Rightarrow 4 x+3 y-\frac{15}{2}=0 \ldots(2)$
Let $d$ be the distance between the lines (1) and (2)
$d=\left|\frac{-11-\left(-\frac{15}{2}\right)}{\sqrt{4^2+3^2}}\right|=\frac{7}{10} \text { units }$
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