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Simar starts from Point A and drives 10 km towards south. He then takes a right turn, drives 7 km, turns right and drives 12 km. He then takes a right turn and drives 9 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.)
2 km to the west
3 km to the west
2 km to the east
3 km to the east
2 km to the west
Track the Cartesian coordinates by assigning North/East as positive and South/West as negative to find net displacement quickly.
Track the Cartesian coordinates by assigning North/East as positive and South/West as negative to find net displacement quickly.
Establish Coordinate System
Starting at Point A (0,0). Move 10 km South: (0, -10). Right turn (West) 7 km: (-7, -10). Right turn (North) 12 km: (-7, 2). Right turn (East) 9 km: (2, 2). Final right turn (South) 2 km: (2, 0). Point P is at (2, 0).
Calculate Net Displacement
Point A is (0,0) and Point P is (2,0). To go from P(2,0) back to A(0,0), Simar must move 2 units in the negative X-direction (West). Thus, he needs to cover 2 km towards the west.
B: 3 km West is incorrect as the X-coordinate difference is only 2; C: 2 km East would take him further away from A; D: 3 km East is incorrect in both magnitude and direction.
A is correct because Point P is located 2 km to the East of Point A (0,0), so traveling 2 km to the West returns Simar exactly to Point A.
Always map turns to the cardinal directions immediately (e.g., facing South, a Right turn is West) to avoid common disorientation errors.
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