Quote: "I need to figure out how far beyond that boundary line point A goes when it rotates."
The post above mine is good; I'll give my own simple crack at it too though. Just calculate the lenght of a line (or the distance) between the pivot point and point A, then draw a line, of that length, straight down from the pivot point. That should be the absolute lowest point A can possibly go below the dotted line.
Another way to look at it (which I am sure you're aware of) is knowing that, as the shape rotates around a specific pivot point, any given point on that shape will just follow a circular path. Hence finding the distance between a given point and the pivot point gives the radius of the circle, center being the pivot point. Then it's easy to visualize how to calculate where things will and won't go.
GI think that's what you were asking. But maybe I'm too tired right now and just took out my contacts so the digital colorful light grid is all fuzzy.

OUT with the ugly campaign signature and IN with some super fancy text.