Mr. Yorly starts from Point A and drives 17 km towards East. He then takes a left turn, drives 18 km, turns left and drives 30 km. He then takes a left turn and drives 31 km. He then takes a left turn, drives 9 km, turns left and drives 6 km. He takes a final right turn, drives 4 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.)
7 km to the North
Taking A as the origin (0, 0) and East as the positive x-axis, North as the positive y-axis:
Drives 17 km East: reaches (17, 0). Turns left, now facing North.
Drives 18 km North: reaches (17, 18). Turns left, now facing West.
Drives 30 km West: reaches (-13, 18). Turns left, now facing South.
Drives 31 km South: reaches (-13, -13). Turns left, now facing East.
Drives 9 km East: reaches (-4, -13). Turns left, now facing North.
Drives 6 km North: reaches (-4, -7). Turns right, now facing East.
Drives 4 km East: reaches Point P at (0, -7).
Point A is at (0, 0), so P is exactly 7 km south of A. To return from P to A, he must drive 7 km to the North.
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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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In which direction is the man facing now?
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