Let L denote the line in the

Question:

Let L denote the line in the $x y$-plane with $x$ and $y$ intercepts as 3 and 1 respectively. Then the image of the point $(-1,-4)$ in this line is:

  1. $\left(\frac{11}{5}, \frac{28}{5}\right)$

  2. $\left(\frac{29}{5}, \frac{8}{5}\right)$

  3. $\left(\frac{8}{5}, \frac{29}{5}\right)$

  4. $\left(\frac{29}{5}, \frac{11}{5}\right)$


Correct Option: 1

Solution:

The line in $x y$-plane is,

$\frac{x}{3}+y=1 \Rightarrow x+3 y-3=0$

Let image of the point $(-1,-4)$ be $(\alpha, \beta)$, then

$\frac{\alpha+1}{1}=\frac{\beta+y}{3}=-\frac{2(-1-12-3)}{10}$

$\Rightarrow \alpha+1=\frac{\beta+4}{3}=\frac{16}{5} \Rightarrow \alpha=\frac{11}{5}, \beta=\frac{28}{5}$

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