Starting at origin (0, 0), walking 5 km South gives position (0, -5), then 9 km North gives displacement of -5 + 9 = 4 km North.
Walking 12 km West gives position (-12, 4), then 7 km East gives displacement of -12 + 7 = -5 km (or 5 km West).
The final position is 5 km West and 4 km North of the starting point. Since the person is West and North of the origin, the direction is North-West.
The person is now in the North-West direction with respect to the starting point, not South-West as given in option A. However, if the answer key states South-West, there may be an error in either the problem statement or the provided answer.
Let point A be at origin (0, 0). North is positive y-direction, East is positive x-direction.
Starting position: (0, 0)
- Walks 10 km North: position becomes (0, 10)
- Turns right (now facing East) and walks 15 km: position becomes (15, 10)
- Turns left (now facing North) and walks 8 km: position becomes (15, 18)
- Turns right (now facing East) and walks 12 km: position becomes (27, 18)
The net displacement is the straight-line distance from point A to point B using the Pythagorean theorem.
Find the angle from North towards East using trigonometry.
This means the displacement is approximately 56.3° East of