2024 AMC 8 Problem 11

The coordinates of \bigtriangleup ABC are A(5, 7), B(11, 7), and C(3, y), with y > 7. The area of \bigtriangleup ABC is 12. What is the value of y?

\textbf{(A)} 8 \qquad \textbf{(B)} 9 \qquad \textbf{(C)} 10 \qquad \textbf{(D)} 11 \qquad \textbf{(E)} 12

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