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 $\large\frac{\pi}{4}$ about the origin of new system in the clockwise direction. The final position of the point (7,5) is

Question

\[(a)\;\bigg[\frac{9}{\sqrt 2},\frac{-1}{\sqrt 2}\bigg] \quad (b)\;\bigg[\frac{7}{\sqrt 2},\frac{1}{\sqrt 2}\bigg] \quad (c)\;\bigg[\frac{7}{\sqrt 2},\frac{-1}{\sqrt 2}\bigg] \quad (d)\;\bigg[\frac{5}{\sqrt 2},\frac{-1}{\sqrt 2}\bigg] \]