Question

Distance between the parallel lines $3x+4y+7=0$and $3x+4y-5=0$ is

• A. $\frac{2}{5}$
• B. $\frac{12}{5}$
• C. $\frac{5}{12}$
• D. $\frac{3}{5}$

Answer 1

The correct option is B

$\frac{12}{5}$

Finding distance between parallel line :

Given: $$\begin{gathered} 3x+4y+7=0\dots \left(i\right) \\ 3x+4y–5=0\dots \left(ii\right) \end{gathered}$$

Distance between two parallel lines,$=\frac{7+5}{\sqrt{3^2+4^2}}$$\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathit{d}\mathbf{=}\frac{{\mathbf{c}}_{\mathbf{1}}\mathbf{-}{\mathbf{c}}_{\mathbf{2}}}{\sqrt{{{\mathbf{a}}_{\mathbf{1}}}^{\mathbf{2}}\mathbf{+}{{\mathbf{b}}_{\mathbf{1}}}^{\mathbf{2}}}}$

$=\frac{12}{5}$

Hence, Option $\left(B\right)$ is correct.