You are facing East. You turn to your left and walk 10 m, then turn to your left and walk 10 m, and then turn \(45^\circ\) to your right and walk straight for 25 m. In which direction are you now from your starting point?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → North-West
A left turn moves the facing direction one step anticlockwise (East → North → West), and a \(45^\circ\) turn moves it half a step, to the direction between two main directions.
Facing East, turns left: now facing North, 10 m: 10 m north of the start
Turns left: now facing West, 10 m: 10 m north, 10 m west
Turns \(45^\circ\) to the right: from West, half a step clockwise towards North, so now facing North-West
25 m towards North-West adds the same distance to the north and to the west: \(25\div\sqrt{2}\approx17.7\) m each
End point: \(10+17.7=27.7\) m north and \(10+17.7=27.7\) m west of the start, equal distances, so exactly on the North-West line
You are North-West of your starting point.
