Distance covered by a vertex of square on tilting it

Question

Square $PQRS$ is tilted $90$ degrees anticlockwise around the point $P$, so that points $Q$, $R$ and $S$ reach to the points $Q'$, $R'$ and $S'$, respectively. What is the distance covered by the point $R$ if the length of $PQ$ is $2$?

Answer is: $\pi\sqrt2$

Cannot seem to visualize his properly.

I have visualized this:

Is this right? I understand it would be a curved path, but have no clue how to approach calculating it.

Answer 1

The distance which the point $R$ covers is equal to a quarter of a circle.

Answer 2

Point $R$ travels on a circle of radius $r=|PR|=\sqrt2|PQ|=2\sqrt2$. The angle of the arc is $\phi=\frac\pi2$, so the distance travelled is $\phi r=\pi\sqrt2$.