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Rohit starts from Point X and drives 8 km towards North. He then takes a left turn, drives 5 km, turns left again and drives 10 km. He takes a final left turn, drives 5 km and stops at Point Y. What is the shortest distance between Point X and Point Y, and in which direction is Point Y with respect to Point X?
2 km, South
2 km, North
5 km, South
3 km, North
2 km, South
Map coordinates using Cartesian offsets: North(+Y), South(-Y), East(+X), West(-X). Net distance is the difference in final coordinates.
Map coordinates using Cartesian offsets: North(+Y), South(-Y), East(+X), West(-X). Net distance is the difference in final coordinates.
Mapping the path from Point X
Start at (0,0). Move 8 km North (0, 8). Left turn means moving West, 5 km (-5, 8). Left turn again means South, 10 km (-5, 8 - 10 = -2). Final left turn means East, 5 km (-5 + 5 = 0, -2).
Determining the final coordinate
After all movements, the final position (Point Y) is (0, -2). Since the X-coordinate is 0, Point Y lies exactly 2 km South of Point X.
B: Incorrect, 2 km North would be at coordinate (0, 2). C: Incorrect, 5 km is the total distance traveled in one axis, not the displacement. D: Incorrect, calculation of total movement ignores the vector cancellation.
A is correct because the final coordinate (0, -2) places Point Y 2 km directly South of the origin (0,0).
In direction problems, always treat moves in opposite directions as subtractions. If moves are equal in magnitude but opposite in direction, they cancel out, simplifying the final position calculation.