1. Suppose f : R2 -> R is a function of two variables. Suppose you are not given a formula for f (x, y), but you are told that if the ordered pairs: (x,, y, ) , (X2, V2), (X3, )/3 ) , and (X4, )4) are the corners of a square in the xy-plane, then y ( x , , y , ) + f ( x 2 , )/2 ) + f ( x3 , )/3 ) + f ( x, , )4) = 0. So, for example, f (0,0) + f (1,0) + f (0,1) + f (1,1) =0 since (0,0), (1,0), (0,1), and (1,1) are the corners of a square in the xy-plane. Prove that it must be the case that f(x, y) = 0 for all (x, y) ER