Step 1: Understanding the Concept:
This problem requires tracking movement on a Cartesian plane (North, South, East, West) and calculating the displacement using the Pythagorean theorem.
Step 2: Key Formula or Approach:
Shortest distance = \(\sqrt{(\text{Net Horizontal Displacement})^2 + (\text{Net Vertical Displacement})^2}\).
Step 3: Detailed Explanation:
1. Ajoy faces East. He walks to his left (North) for 10m.
Current Position: (0, 10), Facing North.
2. He turns left (West) and walks 5m.
Current Position: (-5, 10), Facing West.
3. He turns right (North) and walks 2m.
Current Position: (-5, 12), Facing North.
Net Displacement:
Horizontal (x) = -5m (West).
Vertical (y) = 10 + 2 = 12m (North).
Shortest Distance = \(\sqrt{(-5)^2 + (12)^2} = \sqrt{25 + 144} = \sqrt{169} = 13\)m.
He is currently facing the direction of his last move, which is North.
Step 4: Final Answer:
The shortest distance is 13m and he is facing North.