Question

Image of the point $(-8,12)$ with respect to the line mirror $4x+7y+13=0$ is

• A. $(16,2)$
• B. $(-16,-2)$
• C. $(-12,5)$
• D. $(12,-5)$

Answer 1

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

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

Let $(\alpha ,\beta )$ be image of the point.

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

$\Rightarrow$ $\frac{\alpha +8}{4}=\frac{\beta -12}{7}=\frac{-2\left[4\right(-8)+7(12)+13]}{(4{)}^2+(7{)}^2}$

$\Rightarrow$ $\frac{\alpha +8}{4}=\frac{\beta -12}{7}=\frac{-2(-32+84+13)}{16+49}$

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

$\Rightarrow$ $\frac{\alpha +8}{4}=\frac{\beta -12}{7}=-2$

$\Rightarrow$ $\frac{\alpha +8}{4}=-2$ and $\frac{\beta -12}{7}=-2$

$\Rightarrow$ $\alpha +8=-8$ and $\beta -12=-14$

$\Rightarrow$ $\alpha =-16$ and $\beta =-2$

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