Question

The distance between the lines $3x+4y=9$ and $6x+8y-15=0$ is

• A. $\frac{3}{10}$
• B. $\frac{33}{10}$
• C. $\frac{33}{5}$
• D. none of these

Answer 1

Answer: (A)

$\frac{3}{10}$

For using above formula, have to make coefficient of $x$ & $y$ same.
Multiply by $2$ to first equation
Two equations are
$6x+8y-18=0$
$6x+8y-15=0$

Formula to find distance between two parallel lines:

$=\frac{\left|\right(c2)-(c1\left)\right|}{\sqrt{\left(a^2\right)+\left(b^2\right)}}$
Using formula distance,
$=\frac{\left|\right(-18)-(-15\left)\right|}{\sqrt{\left(6^2\right)+\left(8^2\right)}}=\frac{3}{10}$