The distance between the lines $3 x+4 y=9$ and $6 x+8 y=15$ is

The distance between the lines $3 x+4 y=9$ and $6 x+8 y=15$ is
  1. $\frac{3}{2}$
  2. $\frac{3}{10}$
  3. $6$
  4. $\frac{3}{5}$

Solution

To find, distance between the lines $3 x+4 y=9$ and $6 x+8 y=15$, since we know that distance between the lines $a x+b y+c_1=0$ and $a x+b y+c_2=0$ $\Rightarrow \quad d=\left|\frac{c_1-c_2}{\sqrt{a^2+b^2}}\right|$ Here lines are $3 x+4 y-9=0$ and $3 x+4 y-\frac{15}{2}=0$ $\therefore \quad d=\left|\frac{15 / 2-9}{\sqrt{3^2+4^2}}\right|$ $\begin{aligned} & d=\left|\frac{15-18}{2 \times 5}\right| \\ & d=\frac{3}{10} \text { units }\end{aligned}$

Asked in: AP EAMCET 2021 (23 Aug Shift 2)

Practice more Straight Lines questions on Aicharya