Amit starts from Point Y and drives 14 km towards South. He then turns left and drives 35 km, takes a left and drives 68 km. He then takes a left turn and drives 41 km. He takes a left turn, drives 54 km, turns right and drives 53 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° turns only unless specified.)
59 km towards east
Place Point Y at the origin (0, 0), taking East as positive x and North as positive y.
Drives 14 km South (facing South): position becomes (0, -14).
Turns left (South to East) and drives 35 km: \((0+35,\ -14) = (35,\ -14)\).
Turns left (East to North) and drives 68 km: \((35,\ -14+68) = (35,\ 54)\).
Turns left (North to West) and drives 41 km: \((35-41,\ 54) = (-6,\ 54)\).
Turns left (West to South) and drives 54 km: \((-6,\ 54-54) = (-6,\ 0)\).
Turns right (facing South, right is West) and drives 53 km to Z: \((-6-53,\ 0) = (-59,\ 0)\).
So Z is at (-59, 0) and Y is at (0, 0); both have the same y-coordinate, so Y lies due East of Z at a distance of \(|0-(-59)| = 59\) km.
Hence, Amit should drive 59 km towards east to reach Point Y again.
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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?
