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).
Important Questions from Direction and Distance Turns
Shweta starts walking from her office and walks 150 m towards the south, then she turns right and walks 80 m, and then she turns left and walks 60 m. She finally turns left and walks 280 m to reach a bank. What is the shortest distance between her office and the bank?
Starting from her home, a woman walks 10 km towards the west. She turns left and walks 25 km. Again she turns left and walks 10 km. After that, she again turns left and walks 5 km. How far is she from her house now?
A. 35
B. 20
C. 25
D. 40
A man travels 15 km towards the east, then turns right and travels 20 km. He then turns left and travels 30 km. Finally, he takes a right turn and covers 40 km. The shortest distance between the starting point and the destination is:
A man starts from point ‘O’, travels 20 km towards East to reach point ‘A’, turns right and travels 10 km to reach point 'B', turns right and travels 9 km to reach point 'C', turns right and travels 5 km to reach point 'D', turns left and travels 12 km to reach point 'E' and then turns right and travels 6 km to reach point 'F'.
In which direction is the man facing now?
Lalit walks 9 km east, turns left and walks another 8 km. He again takes a left and walks another 3 km. How far and in which direction is he now from his starting point?
