Shivani moved a distance of 45 meters towards the north. She then turned to the left and walked for about 15 meters, turned left again and walked 50 meters. Finally, she turned to the right at an angle of 45°. In which direction was she moving finally?
(b) South-West
Understanding Direction and Movement Puzzles
This question involves analyzing a sequence of movements and turns to determine the final direction of movement. We need to track Shivani's path step-by-step, noting each turn and its effect on her orientation.
Step-by-Step Movement Analysis
Let's break down Shivani's movements:
- Initial Movement: Shivani starts by moving 45 meters towards the North. Her current direction of movement is North.
- First Turn: She then turns to the left. When moving North, a left turn leads towards the West direction. After this turn, she walks 15 meters, moving towards the West. Her current direction of movement is West.
- Second Turn: She turns left again. When moving West, a left turn leads towards the South direction. After this turn, she walks 50 meters, moving towards the South. Her current direction of movement is South.
- Final Turn: Finally, she turns to the right at an angle of 45°. When moving South, a right turn is towards the West. A 45° right turn from South means turning half-way between South and West. This direction is known as South-West.
Determining the Final Direction
After her final turn, Shivani is moving in the direction that is 45° clockwise (right turn) from South. This direction lies exactly between South and West on a compass rose.
The standard directions are North, South, East, West. The intermediate directions are North-East, South-East, South-West, and North-West. Each intermediate direction is exactly 45° from the two adjacent main directions.
- Turning right from North goes towards East.
- Turning right from East goes towards South.
- Turning right from South goes towards West.
- Turning right from West goes towards North.
Since Shivani was moving South and turned right by 45°, her final direction is South-West.
Summary of Directions
Let's visualize the turns:
| Step | Action | Direction Before Turn | Turn | Direction After Turn |
|---|---|---|---|---|
| 1 | Initial Move | - | - | North |
| 2 | Walk | North | Left (90°) | West |
| 3 | Walk | West | Left (90°) | South |
| 4 | Final Turn | South | Right (45°) | South-West |
Therefore, after all the movements and turns, Shivani was finally moving in the South-West direction.
Revision Table: Key Direction Concepts
| Initial Direction | Turn Left (90°) | Turn Right (90°) |
|---|---|---|
| North | West | East |
| South | East | West |
| East | North | South |
| West | South | North |
A 45° turn moves you halfway towards the next main or intermediate direction. For example, a 45° right turn from South moves you towards West, landing on South-West.
Additional Information: Direction and Angle Basics
Understanding directions and angles is crucial for solving these types of reasoning problems. The four main directions are North, South, East, and West. These are 90° apart from each other.
- North and South are opposite directions.
- East and West are opposite directions.
- East is 90° clockwise from North.
- South is 90° clockwise from East.
- West is 90° clockwise from South.
- North is 90° clockwise from West.
The intermediate directions (North-East, South-East, South-West, North-West) are exactly in the middle of the main directions. North-East is 45° from both North and East.
A 'left' turn or a 'right' turn usually implies a 90° turn unless an angle is specified. When an angle like 45° is specified, you turn exactly by that amount from your current direction.
Important Questions from Direction Sense Test
A man moves to the east side, then turns left, then right, and then further turns right again and then moves left. Now, in which direction is the man?
Sunita rode her scooty Northward, then turned left and then again rode to her left 4 km. She found herself exactly 2 km. West to her starting point. How far did she ride Northwards initially?
Pinky walks a distance 600m towards east, turns left moves 500m, then again turns left and walks 600m and then turns left again and moves 500m and halts. At what distance (in meters) is she from the starting point?
One evening before sunset, two friends Shahrukh and Rakesh were talking to each other face-to-face. If Rakesh’s shadow is exactly to his right side, which direction was Shahrukh facing?
A girl is facing north. She turns 90° in the anti-clockwise direction and then 45° in the clockwise direction. Which direction is she facing now?
