Chapter 5.4, Problem 2MS

Say cheese. You’re making an open-faced cheese sandwich. You are very pleased to discover that your perfectly square slice of processed American cheese product fits exactly over your perfectly square slice of bread. In a moment of inspiration, you decide your sandwich will be even more perfect if you pick up the slice of cheese, rotate it one-quarter of a turn, and then place it back down on the bread. Once you make this final adjustment, will there be a point on the cheese slice that is in exactly the same place it was before you rotated the cheese? If so, describe that point; if not, explain why not.