I never use my mat to measure with. I use only my rulers. I am never sure that the measurements on the mat are true to size. The rulers I am sure of. I will use the lines on the cutting mat to make sure that my fabric is straight before I start cutting, but will never use the mat to measure with, only to cut my material out on.
I am also a right-handed individual and do start cutting on the left side and move to the right.