Problem 19 (2023 AMC 10A)

The line segment from $A(1, 2)$ to $B(3, 3)$ can be transformed to the line segment from $A'(3, 1)$ to $B'(4, 3)$, sending $A$ to $A'$ and $B$ to $B'$, by a rotation centered at the point $P(s, t)$. What is $|s - t|$?