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Anoop starts from Point X and walks 10 m towards the north. He then takes a right turn, walks 6 m, turns right again and walks 14 m. He finally takes a right turn and walks 6 m to stop at Point Y. What is the shortest distance between Point X and Point Y?
4 m
6 m
8 m
10 m
4 m
Track the coordinate movements on a 2D plane: North/South is Y-axis, East/West is X-axis; net displacement is the square root of the sum of squares of net X and net Y distances.
Track the coordinate movements on a 2D plane: North/South is Y-axis, East/West is X-axis; net displacement is the square root of the sum of squares of net X and net Y distances.
Mapping the Path
Starting at X(0,0): 1. Walk 10m North to (0, 10). 2. Turn Right and walk 6m East to (6, 10). 3. Turn Right and walk 14m South to (6, -4). 4. Turn Right and walk 6m West to (0, -4).
Calculating Distance
Point X is (0, 0) and Point Y is (0, -4). The shortest distance is the vertical displacement along the Y-axis. The absolute difference between y-coordinates is |0 - (-4)| = 4 meters.
B: 6m is the horizontal offset, not the final displacement. C: 8m is a common miscalculation if one adds the 6m segments incorrectly. D: 10m is an incorrect sum of partial path segments.
A is correct because the final position Y is 4 meters directly south of starting point X after canceling out the horizontal movements of 6m East and 6m West.
In direction problems, always visualize the path as a series of positive/negative movements on an X-Y axis; orthogonal moves in opposite directions cancel each other out.
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