Trickier this time: you walk 5 km north, 2 km east, 3 km south. How far from start, and in which direction?
Drag the two points
distance = √(2² + 2²) = 2.83
Turn a winding walk into one straight line
- Add up every step north and subtract every step south — that's your y-coordinate.
- Add up every step east and subtract every step west — that's your x-coordinate.
- The straight-line distance home is √(x² + y²).
- The direction home is the bearing of that arrow — drag the point above to see it.
Your turn
Walk 7 km north, 4 km east, 3 km south, 4 km west. Where do you end up?
This is how ships did 'dead reckoning' for centuries: log each leg's direction and length, add up the components, and you know where you are without seeing land.
Vector approach
Net north = 5 − 3 = 2 km. Net east = 2 km. Distance = √(2² + 2²) = √8 ≈ 2.83 km. Bearing: northeast (45°).
Vectors decompose any walk into north/south and east/west. Add the components separately, then Pythagoras.