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Kirti starts from point A and walks 1 km towards east. She takes a right turn and walks 2 km. She then takes a left turn and walks 3 km. She takes a right turn and walks 4 km. She takes a left turn and walks 5 km. She takes a final left turn and walks 6 km to reach a point B. How far (shortest distance) and towards which direction should she walk in order to reach point A again? (All turns are 90 degree turns only unless specified otherwise.)
6 km west
7 km west
9 km west
8 km west
9 km west
Track net movement by separating North-South and East-West coordinates using a Cartesian (X, Y) plane.
Track net movement by separating North-South and East-West coordinates using a Cartesian (X, Y) plane.
Coordinate Mapping
Starting at origin (0, 0): East 1 km (+1, 0). Right turn (South) 2 km (1, -2). Left turn (East) 3 km (4, -2). Right turn (South) 4 km (4, -6). Left turn (East) 5 km (9, -6). Final left turn (North) 6 km (9, 0).
Calculate Displacement
Point B is at (9, 0). To return to Point A (0, 0), one must move from (9, 0) to (0, 0), which is a displacement of 9 km towards the West direction.
A: Incorrect as it undercounts the horizontal distance. B: Incorrect as it miscalculates the cumulative sum of eastward movements. D: Incorrect as it fails to include all eastward vectors (1+3+5=9).
C is correct because the net horizontal displacement is 1 (East) + 3 (East) + 5 (East) = 9 km East, and net vertical displacement is -2 (South) + 4 (South) + 6 (North) = 0, meaning the shortest path to return is 9 km West.
Always treat East/North as positive and West/South as negative to avoid errors in complex multi-turn problems.
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