Mr. Yorly starts from Point A and drives 16 km towards South. He then takes a right turn, drives 14 km, turns right and drives 44 km. He then takes a right turn and drives 2 km, turns right drives 15 km. He then takes a left turn drives 21 km. He takes a final right turn, drives 13 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 West
Take A as origin with East as +x and North as +y, and track the facing direction after each 90° turn.
Drive 16 km South (facing S): position (0, −16).
Right turn (S → W), drive 14 km: position (−14, −16).
Turn right (W → N), drive 44 km: position (−14, 28).
Right turn (N → E), drive 2 km: position (−12, 28).
Turn right (E → S), drive 15 km: position (−12, 13).
Left turn (S → E), drive 21 km: position (9, 13).
Final right turn (E → S), drive 13 km: position (9, 0). This is Point P.
P is at (9, 0) and A is at (0, 0): same y, so P is due East of A by 9 km. To return to A he must drive 9 km towards the West.
Hence the shortest distance is 9 km to the West.
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Important Questions from Direction and Distance
What is the direction of U with respect to P?
What is the shortest distance between R and T?
If a person walks 3m towards the North from point V, takes a right turn and walks for another 15m, which of the following points would he reach?
In which direction is Amit facing at point F?
What is the distance between the starting point and the end point?
