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)