When I want to do perpendicular lines while quilting with rulers I start with my needle down on the line I ended on, then I use a straight ruler that has cross hairs across it's width. I line the cross hairs up on the line I just finished with the ruler against my ruler foot. So I've used the needle location to get my starting point, and the cross hairs on the ruler to keep my ruler lined up perpendicular to the original line. I also will sometimes mark some reference points on the quilt if the line I want to quilt is longer than my ruler, that way I will still have some way of checking my ruler placement if I have to move it along the new line. Hope that makes sense.
Rob