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Vineet starts from Point Y and drives 10 km towards the North. He then takes a right turn, drives 29 km, turns right and drives 34 km. He then takes a right turn and drives 13 km. He takes a final right turn, drives 24 km and stops at Point Z. How far (shortest distance) and towards which direction should he drive in order to reach Point Y again? (All turns are 90 degrees turns only unless specified)
24 km towards the south
19 km towards the east
16 km towards the west
14 km towards the north
16 km towards the west
Track net movements along the Cartesian X and Y axes step-by-step. North/South changes the Y coordinate, East/West changes the X coordinate.
Track net movements along the Cartesian X and Y axes step-by-step. North/South changes the Y coordinate, East/West changes the X coordinate.
Step 1: Track North/South (Y-axis) movements
Vineet drives 10 km North (+10), then turns right (East) and drives 29 km, turns right (South) and drives 34 km (-34), takes a right turn (West) and drives 13 km, and finally takes a right turn (North) and drives 24 km (+24). Net vertical displacement = (+10) - 34 + 24 = 0 km.
Step 2: Track East/West (X-axis) movements
Vineet drives 29 km East (+29) and later drives 13 km West (-13