A person walks 500 m North-East, then 1 km South, turns right to walk another 1 km. Then he walks 500 m South-West and in the end, walks 1 km towards North. Where will he be at the end with respect to the starting position?

Let's track the vectors or geometric properties of each movement phase step-by-step:
1. Move 1: $500\text{m}$ North-East.
2. Move 2: $1\text{km}$ ($1000\text{m}$) South.
3. Move 3: Turn right (since he was traveling South, turning right means moving due West) and walk $1\text{km}$ ($1000\text{m}$).
4. Move 4: $500\text{m}$ South-West.
5. Move 5: $1\text{km}$ ($1000\text{m}$) North.

Geometric cancellation analysis:

* Notice that Move 1 ($500\text{m}$ North-East) and Move 4 ($500\text{m}$ South-West) are exactly equal in distance and precisely opposite in direction. Therefore, these two segments form parallel matching legs that perfectly cancel each other's net displacement out.
* Now, we evaluate the remaining primary cardinal moves: Move 2 ($1\text{km}$ South) and Move 5 ($1\text{km}$ North) are also equal in magnitude and directly opposite, meaning they completely cancel each other out vertically.
The only uncancelled displacement component left is Move 3, which takes him *$1\text{km}$ West**.

Thus, the person will end up exactly $1\text{km}$ West of his starting location.