Question

The line $3x-4y+8=0$ is rotated through an angle $\frac{\pi }{4}$ in the clockwise direction about the point $(0,2)$. The equation of the line in its new position is

• A. $7y+x-14=0$
• B. $7y-x-14=0$
• C. $7y+x-2=0$
• D. $7y-x=0$

Answer 1

The correct option is A $7y+x-14=0$

$\tan \theta =\frac{3}{4},\varphi =\theta +\frac{3\pi }{4}$
$m=\tan \varphi =\tan (\theta +\frac{3\pi }{4})=\frac{\tan \theta -1}{1+\tan \theta }=\frac{\frac{3}{4}-1}{1+\frac{3}{4}}=-\frac{1}{7}$
Equation of $AC$ is $y-2=-\frac{1}{7}(x-0)\Rightarrow x+7y-14=0$