Area of the rhombus bounded by the four lines, $ax\pm by\pm c=0$ is-

The point $\left(4,1\right)$ undergoes the following three transformations successively-

(i) Reflection about the line $y=x$

(ii) Translation through a distance $2$ units along the positive directions of $x$-axis

(iii) Rotation through an angle $\frac{\pi }{4}$ about the origin.

The final position of the point is given by the coordinates: