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Shreya starts from point A and drives 4 km towards the East. She takes three simultaneous left turns and drives 2 km, 2 km and 3 km, respectively. She then takes a right turn and drives 1 km. She takes a final right turn and drives 1 km to reach point B. How far (shortest distance) and towards which direction should she drive to reach Point A again? (All turns are 90 degrees turns only unless specified.)
1 km North
1 km South
1 km East
1 km West
1 km West
Track net displacement on X and Y axes independently: East/West as X, North/South as Y. Sum the vectors to find the final position relative to A.
Track net displacement on X and Y axes independently: East/West as X, North/South as Y. Sum the vectors to find the final position relative to A.
Calculate X displacement (East-West)
Start: 0. East: +4. Three left turns: West (-2), South (no change), East (+0). Right: East (+1). Right: East (+0). Net X = 4 - 2 + 1 = 3 km East.
Calculate Y displacement (North-South)
Start: 0. North/South movements: Left turn 1 (2km North: +2), Left turn 2 (no change), Left turn 3 (3km South: -3), Right turn 1 (0), Right turn 2 (1km North: +1). Net Y = 2 - 3 + 1 = 0.
Result
Net position is 3 km East of A. To return to A, she must travel 3 km West.
A: 1km North is incorrect as Y displacement is 0. B: 1km South is incorrect as Y displacement is 0. C: 1km East is incorrect as the current position is 3km East of origin.
D is correct because the net horizontal displacement is 3 km East and vertical displacement is 0, requiring a 3 km move in the opposite direction (West) to reach Point A.
Always treat North/East as positive and South/West as negative coordinates to simplify complex direction problems into basic arithmetic.
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