2025 Gauss 8 Problem 22

ABCD has vertices A(-3,-2), B(0,r), C(6,10), and D(s,t). AB is parallel to CD, BC is parallel to AD, and r<0. What is the value of r+s+t?

\textbf{(A)}\ 10\quad \textbf{(B)}\ 11\quad \textbf{(C)}\ 12\quad \textbf{(D)}\ 13\quad \textbf{(E)}\ 14

If there are no answer choices shown, enter a numerical answer.

Full credit to this problem is given to the CEMC, you may view all Gauss contests here.