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

1. 7 km south → (0,−7)(0,-7) ( 0 , − 7 )

2. Left (facing south → left = east) 28 km → (28,−7)(28,-7) ( 28 , − 7 )

3. Right (facing east → right = south) 26 km → (28,−33)(28,-33) ( 28 , − 33 )

4. Right (facing south → right = west) 11 km → (17,−33)(17,-33) ( 17 , − 33 )

5. Right (facing west → right = north) 19 km → (17,−14)(17,-14) ( 17 , − 14 )

6. Left (facing north → left = west) 17 km → (0,−14)(0,-14) ( 0 , − 14 )

7. Left (facing west → left = south) 8 km → (0,−22)(0,-22) ( 0 , − 22 ) = point Z

Z is at (0,−22)(0,-22) ( 0 , − 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 .