Question

Find image of a point $(-8,12)$ with respect to line mirror $4x+7y+13=0$.

• A. $(-16,2)$
• B. $(-16,-2)$
• C. $(14,-2)$
• D. $(-14,2)$

Answer 1

The correct option is B $(-16,-2)$

Here $(x_1,y_1)$ is $(-8,12)$

$a=4,b=7$ and $c=13$

$\frac{\alpha +8}{4}=\frac{\beta -12}{7}=\frac{-2\left\{4\right(-8)+12(7)+13\}}{{(-8)}^2+{\left(7\right)}^2}\frac{\alpha +8}{4}=\frac{\beta -12}{7}=\frac{-2\left(65\right)}{65}\Rightarrow \frac{\alpha +8}{4}=-2,\frac{\beta -12}{7}=-2\Rightarrow \alpha =-8-8,\beta =-14+12\Rightarrow \alpha =-16,\beta =-2$

So, the image of the point is $(-16,-2)$.

Option B is correct.