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 $(3,2)$ 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:

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 $(2, 1)$ is translated parallel to the line $L: x - y = 4$ by $2\sqrt{3}$ units. If the new point $Q$ lies in the third quadrant,then the equation of the line passing through $Q$ and perpendicular to $L$ is

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: