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:
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
$\frac{\alpha+1}{1}=\frac{\beta+y}{3}=-\frac{2(-1-12-3)}{10}$
$\Rightarrow \alpha+1=\frac{\beta+4}{3}=\frac{16}{5} \Rightarrow \alpha=\frac{11}{5}, \beta=\frac{28}{5}$