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Suman starts from point A and walks 10 km towards North. She then takes a left turn, walks 5 km, turns right and walks 6 km. She then takes a right turn and walks 5 km. How far (shortest distance) and towards which direction should she move to reach point A again?
16 km, South
16 km, North
12 km, South
12 km, North
16 km, South
Track the net displacement using coordinate geometry: North/South as Y-axis and East/West as X-axis. Sum the movements to find final position (X, Y) relative to origin (0, 0).
Track the net displacement using coordinate geometry: North/South as Y-axis and East/West as X-axis. Sum the movements to find final position (X, Y) relative to origin (0, 0).
Coordinate Mapping
Assume A is at (0, 0). Move 1: 10 km North = (0, 10). Move 2: 5 km Left (West) = (-5, 10). Move 3: 6 km Right (North) = (-5, 16). Move 4: 5 km Right (East) = (0, 16). Suman is at (0, 16).
Calculate Return Path
Suman is currently 16 km North of point A (0, 0). To return to point A, she must move 16 km in the exact opposite direction, which is South.
B: 16 km North would move her further away from point A. C: 12 km South is mathematically incorrect as the total North displacement is 16 km. D: 12 km North is incorrect both in distance and direction.
A is correct because Suman reaches a final position 16 km directly North of point A, necessitating a move of 16 km South to return to the starting point.
In direction problems, always treat the starting point as origin (0,0) and maintain signs for movements to avoid simple addition errors.