There is a large building on fire fire trucks from two different stations respond to the fire one station is 1 mile east and 2 miles north of the fire the other station is 2 miles west and 1 mile south of the fire how far apart are the two fire stations?

An extension of the Pythagorean Theorem is the so-called distance formula.

d^2=(x2-x1)^2+(y2-y1)^2, letting east/west be x, north/sout be y and east and north be positive

d^2=(1--2)^2+(2--1)^2

d^2=3^2+3^2

d^2=9+9

d^2=18

d=√18 mi.

d=√(9*2) mi.

d=3√2 mi.

d≈4.24 mi.  (to nearest hundredth of a mile)