Q.A man walks 4 km towards North, then turns left and walks 4 km, then turns left again and walks 4 km. How far and in which direction is he from his starting point?

Track the net displacement leg by leg, remembering a left turn is a 90-degree anticlockwise turn.

Starting facing North:

• Walks 4 km North.
• Turns left (a left turn from North, turning anticlockwise, points him West).
• Walks 4 km West.
• Turns left again (a left turn from West, turning anticlockwise, points him South).
• Walks 4 km South. …

Confusing 'turn left' with 'turn right' at any one step throws off every direction that follows it — always re-derive the new facing direction carefully at ea …