Mr. Yorly starts from Point A and drives 6 km towards South. He then takes a right turn, drives 37 km, turns right and drives 42 km. He then takes a right turn and drives 47 km. He takes a final right turn, drives 36 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.)
10 km to the West
Take Point A as the origin (0, 0), with north as +y and east as +x.
Drive 6 km south: position becomes (0, −6), facing south.
Right turn (now facing west), drive 37 km: position becomes (−37, −6).
Right turn (now facing north), drive 42 km: position becomes (−37, 36).
Right turn (now facing east), drive 47 km: position becomes (10, 36).
Final right turn (now facing south), drive 36 km: position becomes (10, 0), which is Point P.
P at (10, 0) and A at (0, 0) lie on the same horizontal line, so A is 10 km due west of P.
Hence, he should drive 10 km to the West to reach Point A.
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Important Questions from Direction and Distance Turns
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A. 35
B. 20
C. 25
D. 40
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