A path from (0,0) to (n,n) on the lattice is made up of unit moves upward or rightward. It is balanced if the sum of the x-coordinates of its 2n\plus{}1 vertices equals the sum of their y-coordinates. Show that a balanced path divides the square with vertices (0,0), (n,0), (n,n), (0,n) into two parts with equal area. geometrycalculusintegrationsymmetry