Tamanna is walking towards the north from her house. After 500 metres she turns left and walks for 500 metres. Then she turns left and walks 250 metres to reach her friend’s house. In Which direction is her house from her friend’s house?
South-East
Understanding the Directional Puzzle
This question involves following a set of directions and distances to determine the final position relative to the starting point. We then need to find the direction of the starting point (Tamanna's house) from the final point (her friend's house).
Step-by-Step Analysis of Tamanna's Walk
Let's break down Tamanna's movement:
- Starting Point: Tamanna's house. We can consider this the origin (0,0) for simplicity.
- First Movement: Walks 500 metres towards the North.
New position: 500 metres North of the house. - Second Movement: Turns left and walks for 500 metres. When walking North, a left turn is towards the West.
Movement: 500 metres towards the West.
New position: 500 metres North and 500 metres West of the house. This is her friend's house. - Third Movement: Turns left and walks 250 metres to reach her friend’s house. This step description seems redundant or slightly confusing as she already reached her friend's house after the second movement according to the phrasing "to reach her friend’s house". Let's interpret the second movement as reaching a point, and the third movement from that point leads to her friend's house. However, the question states "Then she turns left and walks 250 metres to reach her friend’s house." This strongly implies the friend's house is after the third segment. Let's re-evaluate based on the phrasing:
Start: House (Origin).
1. North 500m (Point A).
2. From Point A, turn left (West) and walk 500m (Point B).
3. From Point B, turn left (South) and walk 250m to reach friend's house (Point C).
So, the friend's house is at Point C.
Locating the Friend's House Relative to Tamanna's House
Based on the second interpretation:
- Initial movement: North 500m. Let's say this is $+500$ in the y-direction (North). Position after 1st step: $(0, +500)$.
- Second movement: Turn left (West) and walk 500m. This is $-500$ in the x-direction (West). Position after 2nd step: $(-500, +500)$.
- Third movement: Turn left (South) and walk 250m. From West, a left turn is South. This is $-250$ in the y-direction (South). Position after 3rd step (Friend's House): $(-500, +500 - 250) = (-500, +250)$.
So, the friend's house is 500 metres West and 250 metres North of Tamanna's house.
Determining the Direction of Tamanna's House from her Friend's House
We need to find the direction from the friend's house (Point C, which is at $(-500, +250)$ relative to the house) back to Tamanna's house (Origin, which is at $(0,0)$).
To go from $(-500, +250)$ to $(0,0)$, you need to move:
- Horizontally: From $-500$ to $0$, which is $+500$ (East).
- Vertically: From $+250$ to $0$, which is $-250$ (South).
Since the movement required is East and South, the direction of Tamanna's house from her friend's house is South-East.
Summary of Directions
| Step | Direction | Distance | Relative Position (from house) |
|---|---|---|---|
| 1 | North | 500m | 500m North |
| 2 (Turn Left) | West | 500m | 500m West, 500m North |
| 3 (Turn Left) | South | 250m | 500m West, 250m North (Friend's House) |
Friend's house location relative to Tamanna's house: 500m West, 250m North.
Direction of Tamanna's house from Friend's house: To get from West and North position back to origin, move East and South.
The direction is South-East.
Revision Table: Directional Movement Concepts
| Current Direction | Turn Left | Turn Right |
|---|---|---|
| North | West | East |
| East | North | South |
| South | East | West |
| West | South | North |
Additional Information: Relative Direction Explained
When you are asked for the direction of Point A from Point B, you imagine yourself standing at Point B and looking towards Point A. The direction you are facing is the answer.
In this problem, Point A is Tamanna's house and Point B is her friend's house. The friend's house is West and North of Tamanna's house. Therefore, to look from the friend's house back to Tamanna's house, you must look East and South. This combined direction is South-East.
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Directions: Read the information given below carefully and answer the questions accordingly:
Rashmi stepped out of her college and walked 15 m towards South. She then took a left turn and walked 35 m to reach a pastry shop. She then took a right turn and walked 15 m. She then took a right turn and walked 35 m to reach her house. What is the approximate shortest distance between Rashmi's college and her house via the pastry shop?
Important Questions from Direction and Distance Turns
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
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?
A boy starts from his home northward in order to go to a hotel. He took right turn and took left to reach the hotel. Which direction is the hotel facing?
Arun went 6 m from his home towards south and turned left to cover 8 m. Again he turned left and covered 6 m. He again turned right and covered 4 m. What was the direct distance from his home and which direction was he facing?
Sri walked 4 km towards east from home to school, and he turned three times right side of 6 km respectively. What is the distance between his home and the school?
