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Chandan starts from Point A and drives 11 km towards east. He then takes a left turn, drives 8 km, turns left and drives 13 km. He then takes a left turn and drives 13 km. He takes a final left turn, drives 2 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┬░ turns only unless specified.)
5 km to the north
5 km to the south
3 km to the east
3 km to the west
5 km to the north
Track net displacement in X (East-West) and Y (North-South) axes independently; subtract opposing directions to find the final coordinate offset from the start.
Track net displacement in X (East-West) and Y (North-South) axes independently; subtract opposing directions to find the final coordinate offset from the start.
Calculate X-axis (East-West) displacement
Chandan moves 11 km East (+11), 13 km West (-13), and 2 km East (+2). Net displacement = 11 - 13 + 2 = 0 km.
Calculate Y-axis (North-South) displacement
Chandan moves 8 km North (+8) and 13 km South (-13). Net displacement = 8 - 13 = -5 km (meaning 5 km South of Point A).
Determine required return movement
Since Point P is 5 km South of Point A, to return to Point A, he must travel 5 km towards the North.
B: 5 km South would take him further away from the origin. C: 3 km East is incorrect as the X-axis net displacement is 0. D: 3 km West is incorrect as the X-axis net displacement is 0.
A is correct because the cumulative net displacement is 0 km in the X-axis and -5 km in the Y-axis (South), requiring a 5 km movement North to return to the origin.
Always visualize directional problems on a Cartesian plane; treat turns as vector shifts to avoid getting lost in sequential descriptions.
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