Raghav starts from Point A and drives 22 km towards the north. He then takes a left turn, drives 24 km, turns left and drives 38 km. He then takes a left turn and drives 41 km. He takes a final left turn, drives 16 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.)
17 km to the west
Place Point A at the origin (0, 0) and take north as +y and east as +x.
Step 1: 22 km north takes Raghav to (0, 22). He now faces north.
Step 2: A left turn makes him face west; 24 km west gives (−24, 22).
Step 3: A left turn makes him face south; 38 km south gives (−24, −16).
Step 4: A left turn makes him face east; 41 km east gives (17, −16).
Step 5: A final left turn makes him face north; 16 km north gives Point P at (17, 0).
Point A is at (0, 0), so P lies 17 km due east of A; to return, Raghav must drive 17 km straight to the west.
Hence, the shortest distance and direction from P to A is 17 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?
In which direction is Amit facing at point F?
What is the distance between the starting point and the end point?
