2024 AMC 12A Problem 7

In \Delta ABC, \angle ABC = 90^\circ and BA = BC = \sqrt{2}. Points P_1, P_2, \ldots, P_{2024} lie on hypotenuse \overline{AC} so that AP_1= P_1P_2 = P_2P_3 = \ldots = P_{2023}P_{2024} = P_{2024}C. What is the length of the vector sum ?ec{BP_1} + ?ec{BP_2} + ?ec{BP_3} + \ldots + ?ec{BP_{2024}}? \textbf{(A) }1011 \qquad \textbf{(B) }1012 \qquad \textbf{(C) }2023 \qquad \textbf{(D) }2024 \qquad \textbf{(E) }2025 \qquad

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