Question

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

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

Answer 1

Answer: (A)

As $\left(\right.-1,1\left.\right)$ is a point on $3x \, - \, 4y \, + \, 7 \, = \, 0,$ the rotation is possible.
Slope of the given line $=\frac{3}{4}$
Slope of the line in its new position $=\frac{\frac{3}{4} - 1}{1 + \frac{3}{4}}=-\frac{1}{7}$
Therefore, the required equation is $y-1=-\frac{1}{7} \, \left(x + 1\right)$ or $7y+x-6=0$