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Rajat drove for 4 km from point A, towards the west. He took a left turn and drove for 4 km. He took a left turn again and drove for 8 km and then he took a right turn and drove for 3 km. Again, he took a right turn and drove for 4 km. At last, he took a right turn and drove for 6 km and stopped at point B. How far (shortest distance) and towards which direction should he drive in order to reach point A again? (All turns are 90┬░ turns only, unless specified.)
3 km towards the north
2 km towards the south
1 km towards the north
2 km towards the north
1 km towards the north
Assign Cartesian coordinates (X, Y) to each movement: West is -X, East is +X, North is +Y, South is -Y. Sum them up to find the final position relative to A (0,0).
Assign Cartesian coordinates (X, Y) to each movement: West is -X, East is +X, North is +Y, South is -Y. Sum them up to find the final position relative to A (0,0).
Establish Coordinate System
Start at point A(0, 0). West is -X, East is +X, North is +Y, South is -Y.
Calculate Net Displacement
1: West 4km = (-4, 0). 2: Left turn from West is South 4km = (-4, -4). 3: Left turn from South is East 8km = (-4+8, -4) = (4, -4). 4: Right turn from East is South 3km = (4, -4-3) = (4, -7). 5: Right turn from South is West 4km = (4-4, -7) = (0, -7). 6: Right turn from West is North 6km = (0, -7+6) = (0, -1).
Determine Final Position and Return Path
Final position relative to A is (0, -1). This means Rajat is 1 km South of point A. To return to A (0, 0) from (0, -1), one must travel 1 km towards the North.
A: 3 km North leads to position (0, 2), incorrect. B: 2 km South leads to position (0, -3), incorrect. D: 2 km North leads to position (0, 1), incorrect.
C is correct because the net displacement calculation results in a final coordinate of 1 km South of the starting point, requiring a 1 km move North to return to the origin.
When dealing with many turns, always track horizontal (X) and vertical (Y) movements separately to avoid confusion and prevent errors in long sequences.
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