Tracking Ram's Journey Using Coordinates
We can track Ram's movement on a 2D plane. Let Point A be the origin (0, 0). We'll assume North is the positive y-direction and East is the positive x-direction.
- Start: A = (0, 0)
- Move 1: 12 km South. New position: (0, -12).
- Move 2: Turns right (now facing West), drives 7 km. New position: (-7, -12).
- Move 3: Turns left (now facing South), drives 5 km. New position: (-7, -12 - 5) = (-7, -17).
- Move 4: Turns left (now facing East), drives 13 km. New position: (-7 + 13, -17) = (6, -17).
- Move 5: Turns left (now facing North), drives 9 km. New position: (6, -17 + 9) = (6, -8).
- Move 6: Turns left (now facing West), drives 14 km. New position: (6 - 14, -8) = (-8, -8).
- Move 7: Final right turn (now facing North), drives 8 km. New position: (-8, -8 + 8) = (-8, 0).
Calculating Return Path to Point A
Ram's final position is (-8, 0). Point A is at (0, 0).
To find the shortest distance and direction from the final position (-8, 0) back to Point A (0, 0), we need to determine the displacement vector:
Displacement = (Target X - Current X, Target Y - Current Y)
Displacement = (0 - (-8), 0 - 0) = (8, 0)
This vector (8, 0) means Ram needs to move 8 km in the positive x-direction.
- Distance: The magnitude of the displacement vector is $\sqrt{8^2 + 0^2} = \sqrt{64} = 8$ km.
- Direction: A move in the positive x-direction corresponds to East.
Therefore, Ram needs to drive 8 km towards the East to reach Point A again.
Similar Questions
- Xheik starts from Point A and drives 18 km towards East. He then takes a left turn, drives 4 km, turns left and drives 21 km. He then takes a left turn and drives 9 km. He takes a final left turn, drives 3 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.)
- Town N is to the north of Town M. Town O is to the east of Town N. Town P is to the north of Town O. Town Q is to the east of Town P. Town R is to the east of Town Q. What is the position of Town R with respect to Town M?
- Hashini starts from Point Y and drives 16 km towards north. She then takes a left turn, drives 5 km. She then turns left and drives 25 km. She takes a final left turn, drives 5 km and stops at Point Z. How far (shortest distance) and towards which direction should she drive in order to reach Point Y again? (All turns are 90-degree turns only unless specified)
- Vignesh starts from Point Y and drives 17 km towards south. He then takes a left turn, drives 25 km. He then turns right and drives 9 km. He takes a final right turn, drives 25 km and stops at Point Z. How far (shortest distance) and towards which direction should he drive in order to reach Point Y again? (All turns are 90° turns only unless specified.)
- Nilesh starts from Point Y and drives 17 km towards the north. He then takes a left turn and drives 31 km, then turns left and drives 45 km. He then takes a right turn and drives 23 km. He takes a right turn, drives 28 km and stops at Point Z. How far (shortest distance) and in which direction should he drive in order to reach Point Y again? (All turns are 90-degree turns only unless specified.)
- Mohit starts from Point Y and drives 35 km towards north. He then takes a right turn, drives 83 km, turns right and drives 49 km. He then takes a right turn and drives 36 km. He takes a right turn, drives 76 km. He then turns left, drives 47 km, turns left again, drives 21 km and stops at Point Z. How far (shortest distance) and towards which direction should he drive in order to reach Point Y again? (All turns are 90° turns only unless specified.)
- Vinay starts from Point A and drives 8 km towards North. He then takes a left turn, drives 4 km, turns left and drives 11 km. He then takes a left turn and drives 6 km. He takes a final left turn, drives 3 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.)
- Read the given paragraph carefully and answer the question.
Ram walks 5 km straight from his home. After taking a right turn he walks for another 8 km. He then takes a left turn and reaches shop A after 2 km. From there he takes a right turn and walks 2 km. He covers another 7 km to the right to reach shop B.
What is the distance covered by Ram to reach shop A from his home? - John and Jenny stood at a point facing the north. John left Jenny in the morning and walked towards the west for 3 km, taking 15 minutes. Then he moved towards the south for 4 km, taking 25 minutes. What is the shortest distance Jenny needs to travel to meet John?
- From his house, Kamal drives 10 km in the north-west direction and then 10 km in the south-west direction. After that, he drives 10 km in the south-east direction. Finally, he turns towards his house and drives further.
In which of the directions given below is he most likely to be driving?
Important Questions from Direction and Distance
Sita took an auto from her home in Andheri (A) to go to her college in Fatehpuri (F). Rather than continuing straight on the direct road to the college that had no turns, the auto driver took a diversion after 10 km and tumed right at Bandra (B) crossing, then at Colaba T- point (C) after 8 km turned left, again after covering 12 km turned left at Dalhousi Building (D) and soon after 8 km turned right at Elphinston point (E) and after covering 4 km reached Fatehpuri (F). Had the auto driver taken the direct route how much less distance would Sita have actually travelled between the starting point and the destination?
Radha walks a distance of 9 m towards the South-East. Then she walks 15 m towards the West. From here, she walks 9 m towards the North-West. Finally she walks 6 m towards the East and stands at the point. How far is she standing from the starting point?
According to the time by Nihaal's watch its half past one and the hour hand is pointing towards the north-east. Assuming that there is no change in Nihaal's position, in which direction would the minute hand point after 30 minutes?
According to the time by Rohan's watch, it is half past 6 and the watch's hands are pointing to the south. In which of the given directions will the minute-hand point AFTER exactly 24 hours?
According to the time by Rick's watch its quarter past eight. If the minute hand points towards the east, towards which direction would the hour hand point?
