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Anil starts from point A and drives 7 km towards the east. He then takes a left turn, drives 3 km, turns left, and drives 9 km. He then takes a right turn and drives 3 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┬░ turns only, unless specified.)
6 km towards the west
9 km towards the east
6 km towards the south
8 km towards the east
6 km towards the south
Track the net displacement by treating East/North as positive coordinates and West/South as negative coordinates: (East-West) and (North-South).
Track the net displacement by treating East/North as positive coordinates and West/South as negative coordinates: (East-West) and (North-South).
Coordinate mapping
Starting at origin (0, 0): Move 7 km East (+7, 0). Left turn means facing North: 3 km (+7, +3). Left turn means facing West: 9 km (-2, +3). Right turn means facing North: 3 km (-2, +6). Final right turn means facing East: 2 km (0, +6).
Calculate displacement
Point P is at (0, 6) relative to A (0, 0). To return to A (0, 0) from P (0, 6), one must move 6 units in the negative Y-axis direction, which corresponds to 6 km towards the South.
A: 6 km West is incorrect as it results in coordinate (-6, 6) instead of origin. B: 9 km East is incorrect as it results in coordinate (9, 6) instead of origin. D: 8 km East is incorrect as it results in coordinate (8, 6) instead of origin.
C is correct because point P is located 6 km North of point A, therefore to return to point A, one must travel 6 km due South.
In direction problems, always maintain a mental or rough sketch of the X (East-West) and Y (North-South) axes to prevent getting lost in turn sequences.
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