Question

The image of the point $(3,8)$ in the line $x+3y=7$ is :

• A. $(1,4)$
• B. $(4,1)$
• C. $(-1,-4)$
• D. $(-4,-1)$

Answer 1

The correct option is C $(-1,-4)$

Let the image of $(3,8)$ w.r.t. the line mirror $x+3y-7=0$ be $(h,k)$

$\frac{h-p}{a}=\frac{k-q}{b}=\frac{-(a\times p+b\times q+c)}{a^2+b^2}$

$\Rightarrow \frac{h-3}{1}=\frac{k-8}{3}=\frac{-2\left(20\right)}{10}$
$\Rightarrow h-3=\frac{k-8}{3}=-4$
$\Rightarrow h=-1$ and $k=-4$
So, the image is at $(-1,-4)$