Mr. Yorly starts from Point A and drives 9 km towards North. He then takes a left turn, drives 13 km, turns left and drives 19 km. He then takes a left turn and drives 44 km. He takes a final left turn, drives 10 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 degrees turns only unless specified.)
31 km to the West
Use coordinates with East as positive x and North as positive y. Start at A = (0, 0).
Drive 9 km North: reach (0, 9), now facing North.
Left turn faces West, drive 13 km: reach (-13, 9), facing West.
Left turn faces South, drive 19 km: reach (-13, -10), facing South.
Left turn faces East, drive 44 km: reach (31, -10), facing East.
Left turn faces North, drive 10 km: reach (31, 0), which is Point P, facing North.
Point P is at (31, 0) and Point A is at (0, 0). They share the same y-coordinate, so A lies due West of P.
The distance is \(31 - 0 = 31\) km.
Hence, he should drive 31 km to the West to reach Point A.
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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?
