"Displacement" is the straight-line distance and direction between the start-point and the end-point, regardless of what route was taken to get there.
If you draw a picture of how this car traveled, you'll see that it drove along two legs of a right triangle. I'm guessing the driver probably decided to stay on the streets, instead of driving the STRAIGHT line across people's lawns to get to the grocery store. if a BIRD wanted to make the same trip, it would just fly in a straight line, straight over houses and yards.
The bird would fly along the hypotenuse of the right triangle. The distance would be √(3² + 4²).
That's √(9 + 16), which is √(25), and that's 5 km .
'Displacement' is a vector, and it also needs a direction.
After driving 3km north and 4km west, you are 5km roughly Northwest of where you started from. (actually 53.1° west of north)
The car's displacement is 5 km , 53.1° west of north,
or <em>5 km at an azimuth of 306.9°</em> .
