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Vijay starts from point A and drives 10 km towards North. He then takes a left turn, drives 4 km, turns left and drives 12 km. He then takes a left turn and drives 9 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 degrees turns only unless specified)
5 km to the east
4 km to the east
4 km to the west
5 km to the west
5 km to the west
Track the net displacement using a Cartesian plane (North/South = Y-axis, East/West = X-axis). Net change in Y is (10 - 12) = -2 (South), and net change in X is (4 - 9 + 2) = -3 (West).
Track the net displacement using a Cartesian plane (North/South = Y-axis, East/West = X-axis). Net change in Y is (10 - 12) = -2 (South), and net change in X is (4 - 9 + 2) = -3 (West).
Establish Coordinate System
Starting at Point A (0,0). Move 10 km North: Position (0, 10). Left turn (West) 4 km: Position (-4, 10). Left turn (South) 12 km: Position (-4, -2). Left turn (East) 9 km: Position (5, -2). Left turn (North) 2 km: Final Position P is (5, 0).
Calculate Displacement
Point A is at (0, 0) and Point P is at (5, 0). To move from P(5, 0) to A(0, 0), one must move 5 units in the negative X direction, which is 5 km West.
A: 5 km East is incorrect as the displacement vector is -5 (West). B: 4 km East is incorrect as it does not reach the origin (0,0). C: 4 km West is incorrect as it leaves a 1 km gap.
D is correct because Vijay ends at coordinates (5,0) relative to A(0,0), requiring a travel of 5 km West to return to the starting point.
For multi-turn direction questions, always assign positive/negative values to axes (N/E positive, S/W negative) to avoid visual calculation errors.
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