Question

The ratio in which line $3x+4y=2$ divides the distance between $3x+4y=7$ and $6x+8y+19=0$ is:

• A. $10:23$
• B. $23:10$
• C. $13:10$
• D. $10:13$

Answer 1

The correct option is A $10:23$

$\Rightarrow 3x+4y=7\Rightarrow \frac{x}{\frac{7}{3}}+\frac{y}{\frac{7}{4}}=1$

$\Rightarrow 6x+8y+19=0$

$\Rightarrow 3x+4y=\frac{-19}{2}$

Now,

$\Rightarrow \frac{3x}{\frac{-19}{6}}+\frac{4y}{\frac{-19}{2}}=1$

$\Rightarrow \frac{x}{\frac{-19}{6}}+\frac{y}{\frac{-19}{8}}=1$

$\Rightarrow 3x+4y=2$

$\Rightarrow \frac{x}{\frac{2}{3}}+\frac{y}{\frac{1}{2}}=1$

Therefore,

$\Rightarrow d_1=\frac{5}{5}=1$

$\Rightarrow d_2=\frac{2+\frac{19}{2}}{5}=\frac{23}{10}$

Hence, we get

$\Rightarrow \frac{d_1}{d_2}=\frac{1}{\frac{23}{10}}=\frac{10}{23}$

So, option $A$ is correct answer.