I use them also. However I am also left handed. I place the material on the line, the ruler on the material and cut it with my left hand. It works for me.
But I have noticed that the lines are becoming permanent after many years of using only the lines to orient the cuts. Even after I clean the mats the lines are still there. The self cleaning green mats are not as damaged as my large 68 x48 white commercial mat.
MaryKatherine