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Sunny starts from Point A and drives 5 km towards the north. He then takes a left turn, drives 6 km, turns left and drives 7 km. He then takes a left turn and drives 8 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-degree turns only unless specified.)
2 km to the west
3 km to the North
1 km to the east
4 km to the South
2 km to the west
Track net displacement on X and Y axes: North/South as +/- Y and East/West as +/- X to find final coordinates relative to origin.
Track net displacement on X and Y axes: North/South as +/- Y and East/West as +/- X to find final coordinates relative to origin.
Establish Coordinates
Start at Point A (0,0). Move North 5: (0, 5). Turn left (West) 6: (-6, 5). Turn left (South) 7: (-6, -2). Turn left (East) 8: (2, -2). Turn left (North) 2: (2, 0).
Calculate Final Position
Sunny is now at coordinate (2, 0) relative to start (0,0). Since X is +2 (East) and Y is 0, Point P is 2 km East of Point A.
Determine Return Vector
To get from P (2, 0) back to A (0, 0), one must move -2 on the X axis, which is 2 km to the West.
B: 3 km to the North is incorrect as Y-coordinate net result is 0. C: 1 km to the east moves further away from the origin. D: 4 km to the South moves the position into negative Y territory, which is mathematically incorrect.
A is correct because Sunny's final position is 2 km East of Point A, meaning he must travel 2 km to the West to return.
Always draw a quick X-Y coordinate sketch for multi-turn problems; treating North/East as positive and South/West as negative makes calculation error-proof.
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