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.
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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
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?
