Ritwik starts from Point A and drives 46 km towards east. He then takes a right turn, drives 54 km, turns right and drives 56 km. He then takes a right turn and drives 63 km. He takes a final right turn, drives 10 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)
9 km to the south
Take Point A as the origin (0, 0), with east as +x and north as +y.
Drive 46 km east: position becomes (46, 0).
Right turn faces south; drive 54 km south: position becomes (46, −54).
Right turn faces west; drive 56 km west: position becomes (−10, −54).
Right turn faces north; drive 63 km north: position becomes (−10, 9).
Right turn faces east; drive 10 km east: position becomes (0, 9), which is Point P.
Point A is (0, 0) and Point P is (0, 9); they share the same east-west line, and A is 9 km to the south of P.
Hence, Ritwik should drive 9 km to the south to reach Point A again.
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