Since C is 2mi east of A and 2mi south of B, the shortest distance from A to B would be a straight line which is equal to the hypotenuse of a right triangle with a base of 2mi and a height of 2mi..
d^2=x^2+y^2
d^2=2^2+2^2
d^2=4+4
d^2=2*4
d=√(2*4)
d=2√2 mi (exact)
d≈2.83 mi (to nearest hundredth of a mile)
