Arpan starts from Point A and drives 12 km towards East. He then takes a right turn, drives 8 km, turns right and drives 14 km. He then takes a right turn and drives 12 km. He takes a final right 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° turns only, unless specified)
To find the shortest distance and direction back to Point A, let's track Arpan's movement step-by-step using a coordinate system, starting Point A at $(0, 0)$.
Tracking Arpan's Path
Starts at Point A (0, 0).
Drives 12 km East: Moves to $(12, 0)$.
Turns Right (South) and drives 8 km: Moves to $(12, -8)$.
Turns Right (West) and drives 14 km: Moves to $(-2, -8)$.
Turns Right (North) and drives 12 km: Moves to $(-2, 4)$.
Turns Right (East) and drives 2 km: Moves to $(0, 4)$. This is Point P.
Calculating the Return Trip
Arpan is currently at Point P $(0, 4)$ and needs to get back to Point A $(0, 0)$.
Distance: The difference in the y-coordinates is $4 - 0 = 4$ km.
Direction: Since Point A $(0, 0)$ is directly below Point P $(0, 4)$ on the vertical axis, he needs to drive South.
Conclusion
To reach Point A from Point P, Arpan must drive:
4 km to the south
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?
