Question

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

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

Answer 1

Answer: (C)

$(-1,-4)$

Let, $(x_2,y_2)$ be the image, then

$\frac{x_2-3}{1}=\frac{y_2-8}{3}=\frac{-2\cdot (a{x}_1+b{y}_1+c)}{(a^2+b^2)}$

$\Rightarrow x_2-3=\frac{y_2-8}{3}=\frac{-2(3+8\times 3-7)}{(1+9)}=\frac{-2\times 20}{10}=-4$

$\Rightarrow x_2=3-4=-1$

$\Rightarrow y_2=8-3\left(4\right)$

$=-4$

$\therefore (-1,-4)$ is the image.