The origin is translated to $(1,2)$. The point $(7,5)$ in the old system undergoes the following transformations successively.
$I$. Moves to the new point under the given translation of origin.
$II$. Translated through $2$ units along the negative direction of the new $X$-axis.
$III$. Rotated through an angle $\frac{\pi}{4}$ about the origin of the new system in the clockwise direction. The final position of the point $(7,5)$ is

• A
  $\left(\frac{9}{\sqrt{2}}, \frac{-1}{\sqrt{2}}\right)$
• B
  $\left(\frac{7}{\sqrt{2}}, \frac{1}{\sqrt{2}}\right)$
• C
  $\left(\frac{7}{\sqrt{2}}, \frac{-1}{\sqrt{2}}\right)$
• D
  $\left(\frac{5}{\sqrt{2}}, \frac{-1}{\sqrt{2}}\right)$