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Mr. Ok starts from Point O and drives 7 km towards the west. He then takes a right turn, drives 7 km, turns right and drives 2 km. He then takes a left turn and drives 6 km. He then takes a right turn and drives 19 km. He then takes a right turn and drives 16 km. He then takes a final right turn, drives 14 km and stops at Point P. How far (shortest distance) and towards which direction should he drive in order to reach Point O again? (All turns are 90 degrees turns only unless specified.)
4 km towards South
4 km towards East
3 km towards North
3 km towards West
3 km towards North
Calculate net displacement by subtracting opposite directions (East-West and North-South) to find the current coordinate relative to the origin.
Calculate net displacement by subtracting opposite directions (East-West and North-South) to find the current coordinate relative to the origin.
Establish Coordinate System
Set Starting Point O as (0, 0). Move as follows: 1) West 7 km: (-7, 0). 2) Right turn (North) 7 km: (-7, 7). 3) Right turn (East) 2 km: (-5, 7). 4) Left turn (North) 6 km: (-5, 13). 5) Right turn (East) 19 km: (14, 13). 6) Right turn (South) 16 km: (14, -3). 7) Final Right turn (West) 14 km: (0, -3).
Calculate Final Position
After all movements, Point P is at coordinates (0, -3). The Origin O is at (0, 0). The difference is 3 units in the positive Y-direction (North).
A: 4 km South is incorrect as the net vertical displacement is 3 km, not 4 km. B: 4 km East is incorrect as the horizontal displacement is 0. D: 3 km West is incorrect as the current position is South of the origin, requiring a North move to return.
C is correct because the final coordinate is (0, -3) relative to the origin (0, 0), requiring a move of 3 km towards the North to reach Point O.
When tracking long paths, always maintain two separate variables (X for E/W and Y for N/S) to prevent sign errors during complex multi-turn sequences.
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