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Ajit starts from point A and drives 6 km towards North. He then takes two simultaneous left turns and drives 2 km each. He then takes a right turn and drives 3 km. He then takes a left turn and drives 2 km. He takes a final left turn and drives 5 km to reach a point B. 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 South
2 km North
5 km West
3 km South
2 km South
Track the net displacement by assigning signs: North/South as Y-axis (+/-) and East/West as X-axis (+/-).
Track the net displacement by assigning signs: North/South as Y-axis (+/-) and East/West as X-axis (+/-).
Coordinate Mapping
Starting at A(0,0): 1. Move 6km North: (0,6). 2. Two simultaneous left turns (180-degree turn) from North means he is now moving South. Drives 2km each (total 4km): (0, 6-4) = (0,2). 3. Right turn from South is West. Drives 3km: (-3,2). 4. Left turn from West is South. Drives 2km: (-3, 2-2) = (-3,0). 5. Final left turn from South is East. Drives 5km: (-3+5, 0) = (2,0).
Calculate Return Vector
Final position B is at (2,0) relative to A(0,0). To return from (2,0) to (0,0), he must move 2km in the West direction.
B: 2km South is incorrect as the x-coordinate shift is ignored. C: 2km North is incorrect as the vertical net displacement is 0. D: 3km South does not align with the coordinate math.
A is correct because the net displacement calculated from the given route results in point B being 2km to the East of point A, requiring a 2km movement West to return.
When a question involves multiple turns, convert them into a single coordinate plane to avoid confusion from mental visualization.
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