Facing the east R walks straight 4 km, turns left and walks 3 km and a

Facing the east R walks straight 4 km, turns left and walks 3 km and again turns left and walks 4 km. How far is R now from the starting point?

2 km
3 km
10 km
11 km
This question was previously asked in
UPSC CAPF – 2012
R is 3 km away from the starting point.
Let the starting point be the origin (0,0).
1. Walks straight 4 km facing East: Moves to (4, 0).
2. Turns left and walks 3 km: Turning left from East is North. Moves 3 km North from (4, 0), reaching (4, 3).
3. Again turns left and walks 4 km: Turning left from North is West. Moves 4 km West from (4, 3), reaching (4-4, 3) = (0, 3).
The final position is (0, 3) and the starting position is (0, 0). The distance between these points is the y-coordinate, which is 3 km.
This is a basic vector addition problem, or can be solved using coordinates. The path forms a rectangle (4km East, 3km North, 4km West). The endpoint is directly North of the starting point, at a distance equal to the Northward movement.
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