Question:
Let $\mathrm{L}$ denote the line in the $\mathrm{xy}$-plane with $\mathrm{x}$ and $y$ intercepts as 3 and 1 respectively. Then the image of the point $(-1,-4)$ in this line is :
Correct Option: , 3
Solution:
$\mathrm{L}: \frac{\mathrm{x}}{3}+\frac{\mathrm{y}}{1}=1 \Rightarrow \mathrm{x}+3 \mathrm{y}-3=0$
Image of point $(-1,-4)$
$\frac{x+1}{1}=\frac{y+4}{3}=-2\left(\frac{-1-12-3}{10}\right)$
$\frac{x+1}{1}=\frac{y+4}{3}=\frac{16}{5}$
$(x, y) \equiv\left(\frac{11}{5}, \frac{28}{5}\right)$
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