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Gopi starts from Point A and drives 100 km towards East. He then takes a left turn, drives 55 km, turns left and drives 75 km. He then takes a left turn and drives 45 km. He takes a final right turn, drives 25 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.)
8 km towards South
8 km towards North
10 km towards North
10 km towards South
10 km towards South
Map the movements on a Cartesian coordinate plane: East is +X, West is -X, North is +Y, South is -Y. Calculate the net displacement from P back to A (A - P).
Map the movements on a Cartesian coordinate plane: East is +X, West is -X, North is +Y, South is -Y. Calculate the net displacement from P back to A (A - P).
Coordinate Mapping
Starting at A(0,0). 1: 100km East (+100, 0). 2: Left turn (North) 55km (+100, +55). 3: Left turn (West) 75km (+25, +55). 4: Left turn (South) 45km (+25, +10). 5: Right turn (West) 25km (0, +10).
Final Position
After all moves, Gopi is at (0, 10) relative to Point A. This means Point P is 10 km North of Point A.
Required Direction
To return to A(0,0) from P(0, 10), one must travel 10 km in the South direction.
A: 8 km South is incorrect as the calculated distance is 10 km. B: 8 km North is incorrect in both distance and direction. C: 10 km North would take him further away from A.
D is correct because Point P ends up 10 km North of Point A, meaning he must travel 10 km South to return.
Always convert turns into (x,y) movements: North=+y, South=-y, East=+x, West=-x. This eliminates visual confusion.
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