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Manur starts from Point A and drives 12 km towards the East. He then takes a right turn, drives 11 km, turns right and drives 13 km. He then takes a right turn and drives 17 km. He takes a final right turn, drives 1 km and stops at Point P. How far (shortest distance) and towards which direction should he drive in order to reach Point A again? (All turns are 90 degrees turns only unless specified)
2 km to the South
5 km to the South
6 km to the South
3 km to the South
6 km to the South
Track net displacement on X (East-West) and Y (North-South) axes independently; simply reverse the net result to find the return direction.
Track net displacement on X (East-West) and Y (North-South) axes independently; simply reverse the net result to find the return direction.
Coordinate Mapping
Starting at (0,0): 1) East 12km = (12,0). 2) Right (South) 11km = (12,-11). 3) Right (West) 13km = (-1,-11). 4) Right (North) 17km = (-1, 6). 5) Right (East) 1km = (0, 6).
Calculate Displacement
Manur ends at coordinate (0, 6). Point A is at (0, 0). The displacement is 6 km North relative to Point A.
Find Return Direction
To return from (0, 6) to (0, 0), one must travel 6 km in the South direction.
A: 2 km is incorrect as net vertical displacement is 6 km; B: 5 km is incorrect as it does not match the Y-axis delta; D: 3 km is incorrect as it underestimates the total vertical distance.
C is correct because the cumulative movement results in a net position of 6 km North of the starting point, requiring 6 km South to return.
In direction puzzles, always use a simple (X, Y) grid to avoid confusion with consecutive right/left turns.
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