Atharv starts from Point A and drives 12 km towards west. He then takes a right turn, drives 3 km, turns right and drives 16 km. He then takes a right turn and drives 9 km. He takes a final right turn, drives 4 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.)
To solve the problem, we will track the journey step-by-step and calculate the final position relative to the starting point, Point A.
- Atharv starts from Point A, driving 12 km towards the west. His current position is 12 km west of Point A.
- He then takes a right turn and drives 3 km. A right turn from west points north, thus he is now 3 km north from the last position.
- He turns right again and drives 16 km. A right turn from north faces east, so he drives 16 km east.
- He makes another right turn and drives 9 km. This turn takes him south, and he drives 9 km.
- Finally, he turns right and drives 4 km. This last right turn points him west.
Now, let's summarize the distances north-south and east-west:
- East-West direction: \(12 \text{ km west} - 16 \text{ km east} + 4 \text{ km west} = 0 \text{ km}\) (He returns to the original east-west line).
- North-South direction: \(3 \text{ km north} - 9 \text{ km south} = -6 \text{ km}\)
The net effect is that Atharv is 6 km south of Point A, because of the overall southward travel.
Therefore, to return to Point A, Atharv should travel 6 km to the north.
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?
