Karan starts from Point A and drives 12 km towards north. He then takes a left turn, drives 8 km, turns left and drives 14 km. He then takes a left turn and drives 13 km. He takes a final left turn, drives 2 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 degree turns only, unless specified.)
5 km to the west
Take east as +x and north as +y, with A at the origin.
Leg 1: 12 km north → (0, 12), facing north.
Left turn faces west; leg 2: 8 km west → (-8, 12), facing west.
Left turn faces south; leg 3: 14 km south → (-8, -2), facing south.
Left turn faces east; leg 4: 13 km east → (5, -2), facing east.
Left turn faces north; leg 5: 2 km north → P at (5, 0).
So P is 5 km due east of A. To return, Karan must drive 5 km towards the west.
Hence, the required trip is 5 km to the west.
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Important Questions from Direction and Distance
What is the direction of U with respect to P?
What is the shortest distance between R and T?
If a person walks 3m towards the North from point V, takes a right turn and walks for another 15m, which of the following points would he reach?
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What is the distance between the starting point and the end point?
