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Charlie starts from point A and drives 5 km towards the South. He then takes two consecutive right turns and covers distances of 3 km and 2 km, respectively. Finally, he takes a last right turn and drives 3 km to reach point B. What is the minimum distance and in which direction should he drive to return to point A? (All turns are 90 degrees unless otherwise specified.)
2 km East
3 km South
2 km North
3 km North
2 km North
Track the net displacement on X (East/West) and Y (North/South) axes; the direction to return to start is the inverse of the net displacement.
Track the net displacement on X (East/West) and Y (North/South) axes; the direction to return to start is the inverse of the net displacement.
Mapping the path
Start at (0,0). Move 5 km South: (0, -5). Turn Right (facing West) move 3 km: (-3, -5). Turn Right (facing North) move 2 km: (-3, -3). Final Right turn (facing East) move 3 km: (0, -3). This is Point B.
Calculate displacement
Point A is at (0, 0) and Point B is at (0, -3). The difference is 3 km North. To reach A from B (0, -3), Charlie must move 3 km North.
A: Represents an incorrect cardinal direction/distance calculation. B: Represents an incorrect movement vector relative to the origin. C: Incorrectly identifies the return direction.
D is correct because the net displacement from point A is 3 km South, therefore the shortest path to return is 3 km North.
In direction puzzles, always set the starting point as (0,0) and represent every movement as (x, y) coordinates to easily find the final displacement vector.
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