For the digital record, it would be nice if someone would like to answer the question on this slide.
Will the 2D shape remain the same if we scale x, y, and w uniformly?
Yep, as shown on Slide 29.
I think scaling x,y and w uniformly has no effect on the original geometry. Although (x,y,w) and (ax,ay,aw) denotes different point in 2D-H space, they are the same point in the 2D space.