The point (4, 1) undergoes the following transformations successively.

i) Reflection about the line y=x

ii) Translation through 4 units along the positive direction of x-axis.

iii) Rotation through an angle $\frac{\pi }{4}$ about the origin in the clockwise direction. The final position of the point is.

The point (4, 1) undergoes the following transformations 

i) Reflection about the line y=x

$A\left(4,1\right)\to \left(1,4\right)$

ii) Translation through 4 units along the positive direction of x-axis.

$\left(1,4\right)\to \left(5,4\right)$

(iii)

Rotation through an angle $\frac{\pi }{4}$ about the origin in the clockwise direction. The final position of the point is.$\to \left(5+4i\right)e^{-i\pi /4}=\left(5+4i\right)\left(\frac{1-i}{\sqrt{2}}\right)=$$\left(\frac{9}{\sqrt{2}},\frac{-1}{\sqrt{2}}\right)$