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Shahid starts from Point A and drives 20 km towards West. He then takes a left turn, drives 20 km, turns left and drives 15 km. He then takes a left turn and drives 12 km. He takes a final right turn, drives 5 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 otherwise specified.)
10 km towards South
5 km towards North
8 km towards East
8 km towards North
8 km towards North
Track net X and Y coordinates. West is -X, East is +X, North is +Y, South is -Y. Calculate the displacement from P back to A (inverse the sign of the displacement from A to P).
Track net X and Y coordinates. West is -X, East is +X, North is +Y, South is -Y. Calculate the displacement from P back to A (inverse the sign of the displacement from A to P).
Coordinate Mapping
Start at A(0,0). 1) 20km West: (-20, 0). 2) Left turn (South) 20km: (-20, -20). 3) Left turn (East) 15km: (-5, -20). 4) Left turn (North) 12km: (-5, -8). 5) Right turn (East) 5km: (0, -8).
Analyze Final Position P
The final coordinates of Point P are (0, -8) relative to A. This means P is 8km South of A.
Check Path Requirements
Wait, let's re-read the turns: A (0,0) тЖТ 20W (-20,0) тЖТ 20S (-20,-20) тЖТ 15E (-5,-20) тЖТ 12N (-5,-8) тЖТ 5E (0,-8). To get from (0,-8) to (0,0), Shahid must move 8km North.
A: Incorrect distance/direction. B: Incorrect distance. C: Incorrect direction. D: Matches the logic that P is 8km South of A, so he must drive 8km North.
D is correct because Shahid's final displacement from point A is 8km due South, requiring an 8km North movement to return to the origin.
Always convert direction turns (Left/Right) into Cartesian (+X, -X, +Y, -Y) updates to avoid mental mapping errors during complex turns.
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