Question

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

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

Answer 1

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

$m^1=\frac{m-\tan \theta }{1+m\tan \theta }m=3/4$

$=\frac{3/4-\tan \pi /4}{1+3/4\tan \pi /4}$

$=\frac{3/4-1}{1+3/4}$

$m^1=\frac{-1}{7}$

equation $\Rightarrow \frac{y-2}{x-0}=-\frac{-1}{7}$

$7y-14=-x$

$x+7y-14=0$