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
- Vijendra walks a certain distance, say X metres, from his home towards the west. Then he turns left and walks 23 metres. After that, he turns left and walks 36 metres. Then he turns left again to walk 23 metres. He finally turns left and walks 18 metres to reach his home. Find the value of X.
Gaurav exits from the backdoor of his north-facing house and walks 25 m straight, then he takes a left turn and walks 36 m, then he turns left and walks 47 m. He turns left again and walks 36 m. How far and in which direction is he from his house now?
Reeta is standing facing south-east. First, she turns 135° clockwise. After that, she turns 90 ° anticlockwise. Then she turns 45 ° clockwise, followed by a 135 ° anticlockwise turn. In which direction is she facing now?
Sahasra started running from her house towards the north. After 40 meters she turned left and ran for 75 meters. She then turned right and ran for 30 meters, and again turned right to run 75 meters. In which direction was she running finally?
At the time of sunset, Lopa and Kritika are sitting facing each other. If the shadow of Lopa falls to the right of Kritika, in which direction is Kritika facing?
