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

As $(-1,1)$ 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 porition $=\frac{\frac{3}{4}-1}{1+\frac{3}{4}}=-\frac{1}{7}$ 
The required equation is $y-1=-\frac{1}{7}(x+1)$  or   $7y+x-6=0$
Hence , the correct answer is (A)