Town C is 2 miles east of town A and 2 miles south of Town B as in the figure at right. which of the following is the best estimate of the shortest distance from Town A to Town B?

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)