Reshma walked towards the south. After 500 m, she reached her friend Rehana's house. After meeting her friend, Reshma walked towards the east for 500 m, and then turned right and walked for another 500 m. From here, she turned right and walked for 1 km. Finally, she turned to her right and walked for 1 km to reach her college. In which direction is her college from Rehana's house?
North-West
Understanding the Directional Walking Problem
This question asks us to determine the final direction of Reshma's college relative to a specific point: Rehana's house. To solve this, we need to trace Reshma's path segment by segment, noting her movements and turns, and keep track of her position relative to Rehana's house.
Tracing Reshma's Path and Positions
Reshma starts walking south from her home to reach Rehana's house. However, the question asks for the direction from Rehana's house, so we can consider Rehana's house as our starting point or origin for tracing the subsequent path segments.
Let's use a simple coordinate system where Rehana's house is at the origin (0, 0). We'll consider East as the positive x-direction and North as the positive y-direction. Consequently, West is the negative x-direction, and South is the negative y-direction.
Here are the steps Reshma takes from Rehana's house:
- From Rehana's house: Walks towards the east for 500 m.
- Then turns right: Walks for another 500 m (a right turn from East is South).
- From there, turns right: Walks for 1 km (1000 m) (a right turn from South is West).
- Finally, turns to her right: Walks for 1 km (1000 m) to reach her college (a right turn from West is North).
Calculating Final Position Relative to Rehana's House
Let's track Reshma's position using coordinates, starting from Rehana's house at (0, 0):
- Starts at Rehana's house: (0, 0)
- Walks East 500 m: Her position becomes (0 + 500, 0) = (500, 0).
- Turns right (South) and walks 500 m: Her position becomes (500, 0 - 500) = (500, -500).
- Turns right (West) and walks 1 km (1000 m): Her position becomes (500 - 1000, -500) = (-500, -500).
- Turns right (North) and walks 1 km (1000 m): Her position becomes (-500, -500 + 1000) = (-500, 500).
So, Reshma's college is located at the coordinates (-500, 500) relative to Rehana's house.
Determining the Final Direction
The coordinates (-500, 500) mean that the college is 500 units in the negative x-direction (which is West) and 500 units in the positive y-direction (which is North) from Rehana's house.
A position that is both West and North from a reference point is in the North-West direction.
Conclusion: Direction from Rehana's House
Based on the calculations, Reshma's college is located in the North-West direction from Rehana's house.
| Step | Movement from Rehana's House | Change in Position (x, y) | Current Position (x, y) relative to Rehana's House |
|---|---|---|---|
| Start | At Rehana's House | (0, 0) | (0, 0) |
| 1 | 500 m East | (+500, 0) | (500, 0) |
| 2 | 500 m South (Turn Right from East) | (0, -500) | (500, -500) |
| 3 | 1 km (1000 m) West (Turn Right from South) | (-1000, 0) | (500 - 1000, -500) = (-500, -500) |
| 4 | 1 km (1000 m) North (Turn Right from West) | (0, +1000) | (-500, -500 + 1000) = (-500, 500) |
Revision Table: Key Steps and Positions
| Location | Position Relative to Rehana's House (Approximate) | Direction from Rehana's House |
|---|---|---|
| Rehana's House | (0, 0) | - |
| After 500m East | (500, 0) | East |
| After 500m South | (500, -500) | South-East |
| After 1km West | (-500, -500) | South-West |
| College | (-500, 500) | North-West |
Additional Information: Understanding Relative Direction
Finding direction "from X" means imagining yourself standing at point X and looking towards the final destination. In this problem, Rehana's house is point X. We found the college was 500m West and 500m North from Rehana's house, placing it squarely in the North-West quadrant relative to that point.
Using a coordinate system is a helpful method for solving such spatial reasoning problems involving multiple turns and distances. It allows for a systematic way to track the position changes in two dimensions (East-West and North-South).
Similar Questions
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Important Questions from Direction and Distance Turns
After leaving school, Hemant and Anurag walk towards the north for 1 km to reach a bus stop. From the bus stop, Hemant turns left and walks for 500 m. Then he turns towards his left and walks for 2 km to reach his home. From the bus stop, Anurag turns right and walks for 250 m. Then he turns right and walks for 1 km to reach his home. In which direction is Anurag's home from Hemant's home?
A bank employee drives 10 km towards South from her house and turns to her left and drives another 20 km. She again turns left and drives 40 km, then she turns to her right and drives for another 5 km. She again turns to her right and drives another 30 km to reach her bank where she works. What is the shortest distance between her bank and her house ?
A woman runs 12 km towards her North, then 6 km towards her South and then 8 km towards her East. In which direction is she from her starting point ?
Two friends Xand Ystart running and they run together for 50 m in the same direction and reach a point. Xturns right and runs 60 m, while Yturns left and runs 40 m. Then Xturns left and runs 50 m and stops, while Yturns right and runs 50 m and then stops. How far are the two friends from each other now?
Shekhar starts walking south from his school and then took one right turn, one left turn and one right turn to reach his shop. In which direction is Shekhar with respect to his school?
