Mr. Z starts from Point Y and drives 3 km towards South. He then takes a left turn, drives 6 km, turns left and drives 9 km. He then takes a left turn and drives 15 km. He takes a final left turn, drives 6 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)
9 km towards East
Take Point Y as the origin (0, 0), with East as +x and North as +y.
3 km South → (0, −3). Facing South, a left turn means facing East: 6 km → (6, −3).
Left turn → facing North: 9 km → (6, 6).
Left turn → facing West: 15 km → (−9, 6).
Left turn → facing South: 6 km → (−9, 0). This is Point Z.
Point Z is 9 km directly West of Point Y (same y-coordinate), so he must drive 9 km towards East to return.
Hence, he should drive 9 km towards East.
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Important Questions from Direction and Distance
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drives 7 km, turns right and drives 5 km. He then takes a left turn and drives 9 km. He
takes a final right turn, drives 7 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
$90^{\circ}$ turns only unless specified.)
