Question
Vijay starts from point Y and drives 7 km towards South.
He then takes a left turn, drives 28 km, turns right and drives 26 km. He then takes a right turn and drives 11 km. He takes a right turn, drives 19 km. He then turns left, drives 17 km, and turns left and drives 8 km to stop 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 degree turns only unless specified.)Solution
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7 km south β (0,β7)(0,-7) ( 0 , β 7 )
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Left (facing south β left = east) 28 km β (28,β7)(28,-7) ( 28 , β 7 )
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Right (facing east β right = south) 26 km β (28,β33)(28,-33) ( 28 , β 33 )
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Right (facing south β right = west) 11 km β (17,β33)(17,-33) ( 17 , β 33 )
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Right (facing west β right = north) 19 km β (17,β14)(17,-14) ( 17 , β 14 )
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Left (facing north β left = west) 17 km β (0,β14)(0,-14) ( 0 , β 14 )
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Left (facing west β left = south) 8 km β (0,β22)(0,-22) ( 0 , β 22 ) = point Z
Z is at (0,β22)(0,-22) ( 0 , β 22 ) and Y is at (0,0)(0,0) ( 0 , 0 ) . The shortest route from Z to Y is a straight line of length 2222 22 km due north . Answer: He should drive 22 km north .
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