Mr. Jigmee starts from Point A and drives 29 km towards the west. He then takes a left turn, drives 11 km, turns left and drives 46 km. He then takes a left turn, drives 36 km, turns left and drives 5 km. He then takes a left turn and drives 9 km. He takes a final right turn, drives 12 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° turns only unless specified.)
16 km to the south
Place Point A at the origin and take east as positive x and north as positive y. Track the facing direction after each 90° turn.
Drive 29 km west (facing west): position becomes \((-29,\ 0)\).
Left turn while facing west means now facing south; drive 11 km south to reach \((-29,\ -11)\).
Left turn while facing south means now facing east; drive 46 km east to reach \((17,\ -11)\).
Left turn while facing east means now facing north; drive 36 km north to reach \((17,\ 25)\).
Left turn while facing north means now facing west; drive 5 km west to reach \((12,\ 25)\).
Left turn while facing west means now facing south; drive 9 km south to reach \((12,\ 16)\).
Right turn while facing south means now facing west; drive 12 km west to reach Point P at \((0,\ 16)\).
Point A is at \((0,\ 0)\) and P is at \((0,\ 16)\), so P is due north of A by 16 km. To return, Jigmee must drive 16 km due south.
Hence, the shortest distance is 16 km to the south.
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