Question

The line $3x-4y+8=0$ is rotated through an angle $\frac{\pi }{4}$ in the clockwise sense about the point $(0,2)$ 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 $x+7y-14=0$

$m_1=\tan \theta =3/4$

$m_2=\frac{m_1-\tan \pi /4}{1+m_1\tan \pi /4}=\frac{3/4-1}{1+3/4}=\frac{-1}{7}$

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

$7y-14=-x$

$x+7y-14=0$