Social Distancing Squared

Four benches are arranged in a square, and four people sitting on the benches have to maintain a 6-ft safe distance as they all slide along the benches. Where can they sit? Where can they not sit? This set of problems gives a fresh twist on min-max type problems involving Pythagorean Theorem expressions. The problem is layered, which means that you can use it with some classes in its entirety but use only some of the challenges with other classes.