2023 AMC 10A Problem 19

The line segment formed by A(1, 2) and B(3, 3) is rotated to the line segment formed by A'(3, 1) and B'(4, 3) about the point P(r, s). What is |r - s|?

\textbf{(A)} \dfrac{1}{4} \qquad \textbf{(B)} \dfrac{1}{2} \qquad \textbf{(C)} \dfrac{3}{4} \qquad \textbf{(D)} \dfrac{2}{3} \qquad \textbf{(E)} 1

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.