Pooja started from point A and walked 15 feet in the north -east direction to reach point B. She then took a 270° anti-clockwise turn and walked 5 feet to reach point C. After that, she took a 90° clockwise turn and walked 18 feet to reach point D. She continued walking in the same direction after reaching point D. In which direction is she finally walking towards?
South-West
Understanding the Direction Problem
This question involves tracking Pooja's movement and changes in direction based on specific turns. We need to determine her final walking direction after a series of steps and turns.
Analyzing Pooja's Movement Step-by-Step
Let's break down Pooja's journey and how her direction changes at each point:
- Starting from Point A: Pooja starts at point A and walks 15 feet in the north-east direction to reach point B. Her initial direction is North-East.
-
At Point B (First Turn): At point B, she takes a 270° anti-clockwise turn.
- The current direction is North-East.
- An anti-clockwise turn of 270° is equivalent to a clockwise turn of 360° - 270° = 90°.
- From North-East, a 90° clockwise turn leads to the South-East direction.
- So, the direction from B to C is South-East. She walks 5 feet in this direction.
-
At Point C (Second Turn): At point C, she takes a 90° clockwise turn.
- The current direction is South-East (from B to C).
- From South-East, a 90° clockwise turn leads to the South-West direction.
- So, the direction from C to D is South-West. She walks 18 feet in this direction.
- After Point D: She continues walking in the same direction after reaching point D. The direction she was walking in from C to D is South-West.
Determining the Final Direction
Since Pooja continues walking in the same direction after reaching point D, her final walking direction is the direction she moved from C to D. As determined in the previous step, this direction is South-West.
Summary of Direction Changes
| Segment | Starting Direction | Turn | Turn Type | Ending Direction |
|---|---|---|---|---|
| A to B | Start | N/A | N/A | North-East |
| B to C | North-East | 270° | Anti-clockwise | South-East |
| C to D | South-East | 90° | Clockwise | South-West |
| After D | South-West | None | None | South-West |
Therefore, Pooja is finally walking towards the South-West direction.
Revision Table: Key Concepts
| Concept | Explanation |
|---|---|
| Cardinal Directions | North, East, South, West. |
| Intercardinal Directions | North-East, South-East, South-West, North-West. These are halfway between cardinal directions. |
| Clockwise Turn | Turning in the same direction as clock hands (e.g., North > East > South > West). |
| Anti-clockwise Turn | Turning in the opposite direction of clock hands (e.g., North > West > South > East). |
| Degrees in a Full Circle | A full circle is 360°. A 90° turn moves one full cardinal or intercardinal direction. |
Additional Information: Directional Reasoning
Direction and distance problems are common in reasoning sections of competitive exams. They test your ability to visualize movement and turns in a plane. Understanding the relationship between degrees and directional changes is crucial. For example:
- A 90° turn changes direction by one major step (e.g., North to East, or North-East to South-East).
- A 180° turn reverses the direction (e.g., North to South, North-East to South-West).
- A 270° anti-clockwise turn is the same as a 90° clockwise turn.
- A 270° clockwise turn is the same as a 90° anti-clockwise turn.
Always visualize the compass and track the turns relative to the current direction. Pay close attention to whether the turn is clockwise or anti-clockwise and the number of degrees.
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?
