Ravi walks 10 km north, turns right and walks 6 km, then turns right again and walks 18 km. How far is he from his starting point, and in which direction?

Direction problems become easy if you track position as two numbers: how far east (or west) and how far north (or south). Each turn changes the direction you face; "right" from north is east, right from east is south. At the end, combine the east-west and north-south totals with Pythagoras.

Question: 10 km north, right, 6 km, right, 18 km.

Start at (0, 0), with x east and y north.

1. 10 km north: (0, 10). Facing north.
2. Turn right: now facing east. 6 km: (6, 10).
3. Turn right: now facing south. 18 km: (6, -8).
4. Distance = square root of (36 + 64) = 10 km.
5. He is east (x positive) and south (y negative): south-east of the start.

const x = 6, y = 10 - 18;
console.log(Math.hypot(x, y)); // Output: 10
console.log(y < 0 && x > 0 ? "south-east" : "other"); // Output: south-east

Right turns go clockwise: N, E, S, W. Left turns go anticlockwise: N, W, S, E.

• Adding all distances (34 km) instead of finding the straight-line distance.
• Turning right from east and going north instead of south.