Question

The line $3x-4y+7=0$ is rotated through an angle $\frac{\pi }{4}$ in clockwise direction about the point $(1,1)$. The equation of the line in its new position is

• A. $7y+x-6=0$
• B. $7y-x-6=0$
• C. $x+7y=8$
• D. $7y-x+6=0$

Answer 1

Answer: (A)

$7y+x-6=0$

Given slope $=\frac{3}{4}<1$

$<{45}^o$

$\therefore$ after rational clock slope because negative

$\frac{m_1-m_2}{1+m_1,m_2}=\tan 45$

$m_1=\frac{3}{4}{m}_2=$ new slope

$\left|\frac{\frac{3}{4}-m}{1+\frac{3}{4}m}\right|=1$

$\frac{3}{4}-m=\pm (1+\frac{3}{4}m)$

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

$\frac{7}{4}m=\frac{-1}{4}$

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

$\therefore$ satisfy slope and pt in option to save time.