Question

Find the image of the point $(4,-13)$ with respect to the line mirror $5x+y+6=0$

• A. $(\frac{3}{2},\frac{-27}{2})$
• B. $(\frac{-3}{2},\frac{27}{2})$
• C. $(-1,-14)$
• D. $(1,14)$

Answer 1

The correct option is C $(-1,-14)$

Let the image of $(4,-13)$ w.r.t. the line mirror $5x+y+6=0$ be $(h,k)$
$\Rightarrow \frac{h-4}{5}=\frac{k+13}{1}=\frac{-2\left(13\right)}{13}$
$\Rightarrow \frac{h-4}{5}=\frac{k+13}{1}=-1$
$\Rightarrow \frac{h-4}{5}=-1$ and $\frac{k+13}{1}=-1$
$\Rightarrow h=-1,k=-14$
So, the image is at $(-1,-14)$