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Devansh starts from point A and drives 10 km towards the North. He takes two simultaneous right turns and drives 3 km and 6 km, respectively. He takes a final right turn and drives 3 km to reach point B. How far (shortest distance) and towards which direction should he drive to reach Point A again? (All turns are 90 degrees turns only unless specified.)
3 km East
4 km North
6 km South
4 km South
4 km South
Track the net horizontal and vertical displacements separately using a Cartesian coordinate system (Start = 0,0).
Track the net horizontal and vertical displacements separately using a Cartesian coordinate system (Start = 0,0).
Mapping the path
Start at (0,0). Move 10 km North: (0, 10). Two right turns: 1st turn East (3 km) gives (3, 10); 2nd turn South (6 km) gives (3, 4). Final right turn West (3 km) gives (0, 4) at point B.
Calculate distance and direction
Point B is at (0, 4) and A is at (0, 0). The difference is 4 km North. To reach A from B, he must move in the opposite direction (South) by the same distance (4 km).
A: Incorrect distance (3km). B: Incorrect distance (4km) and wrong direction (North instead of South). C: Incorrect distance (6km).
D is correct because point B is exactly 4 km North of point A, meaning one must travel 4 km South to return to A.
In direction problems involving multiple turns, always use a fixed origin (0,0) and track X (East/West) and Y (North/South) coordinates separately.
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