2024 AMC 12A Problem 7

\triangle 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=\cdots=P_{2023}P_{2024}=P_{2024}C

. What is the length of the vector sum

\overrightarrow{BP_1}+\overrightarrow{BP_2}+\overrightarrow{BP_3}+\cdots+\overrightarrow{BP_{2024}}?

\text{(A)}\;1011

\text{(B)}\;1012

\text{(C)}\;2023

\text{(D)}\;2024

\text{(E)}\;2025