Dinesh starts from Point A and drives 20 km towards West. He then takes a left turn, drives 18 km, turns left and drives 21 km. He then takes a left turn and drives 28 km. He takes a final left turn, drives 1 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° turns only unless specified.)
10 km to the South
Take East as +x and North as +y, and start at A = (0, 0).
Drive 20 km West: facing West, move to (−20, 0).
Left turn from West faces South; drive 18 km: (−20, −18).
Left turn from South faces East; drive 21 km: (−20+21, −18) = (1, −18).
Left turn from East faces North; drive 28 km: (1, −18+28) = (1, 10).
Left turn from North faces West; drive 1 km: (1−1, 10) = (0, 10) = Point P.
Point A is at (0, 0) and P is at (0, 10). The x-coordinates match, so A is due South of P at a distance of 10 km.
Hence, Dinesh must drive 10 km to the South.
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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?
In which direction is Amit facing at point F?
What is the distance between the starting point and the end point?
