I'm getting introduced to modes and got a small homework assignment to identify the modes of some short melodies. The problem is I'm not sure that I'm following the guideline correctly, and I can't ask my teacher because he's currently on a leave and I have to upload the solution to the school's website.
I solved it as if the last note, B flat, was the "root" of the mode and find its relations with the other notes, which would mean the first melody (I think) is in Dorian mode. Am I doing it correctly? In general does "do" represent the root/tonic of a scale or a mode?