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)

A