Step 1: Understanding the Concept:
Use the Pythagorean theorem ($a^2 + b^2 = c^2$) to find the displacement from the origin.
Step 2: Identifying the Vector of Change:
- Move 1: 12 km North.
- Move 2: 4 km East (Turn right from North).
- Move 3: 9 km South (Turn right from East).
Step 3: Calculation:
- Net Vertical distance = $12 \text{ (North)} - 9 \text{ (South)} = 3 \text{ km North}$.
- Net Horizontal distance = $4 \text{ km East}$.
- Distance = $\sqrt{3^2 + 4^2} = \sqrt{9 + 16} = \sqrt{25} = 5 \text{ km}$.
- Direction: Since he is North and East of the start, it is North-East.
Step 4: Final Answer:
Samesh is 5 km North-East from the starting point. Thus, the correct option is (d).