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Anu starts from Point A and drives 3 km towards the north. He then takes a right turn, drives 2 km, turns right and drives 5 km. He then takes a right turn and drives 4 km. He takes a final right 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-degree turns only unless specified.)
6 km to the east
4 km to the west
2 km to the east
8 km to the North
2 km to the east
Track the Cartesian coordinates (X, Y) starting at origin (0,0). Each right turn changes direction clockwise: North тЖТ East тЖТ South тЖТ West.
Track the Cartesian coordinates (X, Y) starting at origin (0,0). Each right turn changes direction clockwise: North тЖТ East тЖТ South тЖТ West.
Coordinate Mapping
Starting at (0,0): Move North 3km (0,3). Right turn East 2km (2,3). Right turn South 5km (2,-2). Right turn West 4km (-2,-2). Final right turn North 2km (-2,0).
Final Position Calculation
Final point P is at (-2, 0) relative to start point A (0,0). To return from (-2,0) to (0,0), Anu must move +2 in the X direction (East).
A: 6 km East is incorrect as the displacement is only 2 km. B: 4 km West is incorrect as it increases the distance from A. D: 8 km North is incorrect as the Y-axis displacement is already zero.
C is correct because the coordinate analysis shows Point P is 2 km west of Point A, requiring a 2 km drive east to return to the starting point.
In any direction problem, assume the start point is (0,0) and track the X and Y net changes to avoid visual estimation errors.
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