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Rohan starts from Point X and drives 5 km towards the East. He then takes a left turn, drives 12 km, turns left and drives 5 km. He then takes a final right turn and drives 3 km to reach Point Y. How far (shortest distance) and towards which direction should he drive to reach Point X again from Point Y?
15 km, South
15 km, North
12 km, South
12 km, North
15 km, South
Track the net vertical (North-South) and horizontal (East-West) displacement separately using signs: (+X=East, -X=West, +Y=North, -Y=South).
Track the net vertical (North-South) and horizontal (East-West) displacement separately using signs: (+X=East, -X=West, +Y=North, -Y=South).
Calculate movement in Cartesian coordinates
Start at (0,0). Move 5 km East: (5,0). Turn left (North) for 12 km: (5,12). Turn left (West) for 5 km: (0,12). Turn right (North) for 3 km: (0,15).
Determine final coordinates and distance
Point Y is at (0,15). Point X is at (0,0). The shortest distance is the straight line from Y to X, which is 15 km. Since X is at (0,0) and Y is at (0,15), moving from Y to X requires moving 15 km due South.
B: 15 km North is incorrect as Y is north of X, so returning to X requires moving South. C: 12 km is an incomplete vertical calculation ignoring the final 3 km leg. D: 12 km North is mathematically inconsistent with the net Y-axis displacement of 15 km.
A is correct because the final position of Y is 15 km directly North of X, necessitating a 15 km movement in the South direction to return to X.
In direction problems, always sum up total North-South movements and total East-West movements separately to find net displacement from the origin.