Raj is facing north. He cycles for 8 km, then turns towards the south-east direction to move 10 km and from there, he moves 6 km towards the west. In which direction/place is he from his original position?

Let's map Raj's movements step-by-step using a Cartesian coordinate system, starting from the origin (0,0):
Starts at (0,0) facing North.

Moves 8 km North → New position is (0,8).

Turns South-East and moves 10 km.

South-East direction forms a right-angled triangle with the vertical (South) and horizontal (East) displacement.

Since he goes 10 km hypotenuse diagonally downward towards south-east from (0,8), let's check if it forms a standard (6,8,10) Pythagorean triple.

If he moves 8 km down (South) and 6 km right (East), the distance is
8
2
+6
2


​
=10 km.

Moving 8 km South from (0,8) brings his y-coordinate back to 8−8=0.

Moving 6 km East brings his x-coordinate to 0+6=6.

So, after moving 10 km South-East, his position is exactly (6,0).

Moves 6 km towards the West.

From (6,0), moving 6 km West means subtracting 6 from the x-coordinate: 6−6=0.

His final position is (0,0).

Thus, Raj is exactly at the original position.