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Rahul starts from Point X and drives 8 km towards North. He then takes a left turn, drives 5 km, turns left and drives 12 km. He then takes a left turn and drives 5 km. He takes a final left turn, drives 4 km and stops at Point Y. How far and in which direction is Point Y from Point X?
0 km
4 km, North
4 km, South
8 km, West
0 km
Track the Cartesian coordinates by adding North/South and East/West movements separately. If North movements equal South and East movements equal West, the displacement is zero.
Track the Cartesian coordinates by adding North/South and East/West movements separately. If North movements equal South and East movements equal West, the displacement is zero.
Establish Starting Point
Let Point X be at coordinates (0, 0).
Calculate Sequential Movements
Start (0,0). Move North 8 km: (0, 8). Turn Left (West) 5 km: (-5, 8). Turn Left (South) 12 km: (-5, -4). Turn Left (East) 5 km: (0, -4). Turn Left (North) 4 km: (0, 0).
Verify Final Position
The final coordinate is (0, 0), which is exactly Point X. Thus, the distance is 0 km.
B: 4 km, North is incorrect as the final net displacement in North-South is zero. C: 4 km, South is incorrect as the final net displacement in North-South is zero. D: 8 km, West is incorrect as the East-West horizontal displacement sums to zero (-5 + 5 = 0).
A is correct because the net algebraic sum of movements along both the North-South axis (+8-12+4=0) and the East-West axis (-5+5=0) results in zero displacement from the starting point.
When a question involves multiple turns of the same angle (e.g., all 90-degree left turns), use the coordinate method to avoid losing track of the path orientation.
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