Let $A = (2, 0)$ and $B = (6, 4)$ be two points. If the line segment $\overline{AB}$ is rotated about $A$ through an angle of $45^{\circ}$ in the negative (clockwise) direction,then the coordinates of $B$ after the rotation are:

The point $(4, 1)$ undergoes the following three transformations:
$(i)$ Reflection about the line $y = x$.
$(ii)$ Translation by $2$ units along the positive direction of the $x$-axis.
$(iii)$ Rotation about the origin by an angle of $\pi/4$ in the counter-clockwise direction.
Find the coordinates of the final position of the point.

The point $(3,2)$ undergoes the following three transformations in the order given:
$(i)$ Reflection about the line $y=x$.
(ii) Translation by the distance $1$ unit in the positive direction of $x$-axis.
(iii) Rotation by an angle $\frac{\pi}{4}$ about the origin in the anti-clockwise direction.
Then,the final position of the point is:

The line joining the points $A(2,0)$ and $B(3,1)$ is rotated through an angle of $45^{\circ}$ about $A$ in the anti-clockwise direction. Find the coordinates of $B$ in the new position.

The point $(4,1)$ undergoes the following transformations successively:
$I$. Reflection about the line $y=x$.
$II$. Translation through a distance $2$ units in the direction of the positive $X$-axis.
$III$. Rotation through an angle $\frac{\pi}{4}$ about the origin in the anticlockwise direction.
Then,the final position of the point is: