Reeta is standing facing south-east. First, she turns 135° clockwise. After that, she turns 90 ° anticlockwise. Then she turns 45 ° clockwise, followed by a 135 ° anticlockwise turn. In which direction is she facing now?
East
Solving Direction and Turn Reasoning Questions
Direction and turn questions test your spatial reasoning ability. To solve these problems, it's helpful to visualize the standard directions and understand how turns (clockwise and anticlockwise) affect the facing direction.
The standard directions are North, South, East, and West. The intercardinal directions are North-East, South-East, South-West, and North-West.
- An angle of $45^{\circ}$ separates a main direction from an adjacent intercardinal direction (e.g., North and North-East).
- An angle of $90^{\circ}$ separates two adjacent main directions (e.g., North and East) or two adjacent intercardinal directions (e.g., North-East and South-East).
Step-by-Step Analysis of Reeta's Turns
Let's track Reeta's facing direction after each turn starting from South-East.
Initial Direction: South-East
Turn 1: $135^{\circ}$ clockwise from South-East.
- From South-East, $45^{\circ}$ clockwise is South.
- From South, $90^{\circ}$ clockwise is West ($45^{\circ}$ to South-West, then $45^{\circ}$ to West).
- Total clockwise turn: $45^{\circ} + 90^{\circ} = 135^{\circ}$.
- After Turn 1, Reeta is facing West.
Turn 2: $90^{\circ}$ anticlockwise from West.
- From West, $90^{\circ}$ anticlockwise is South ($45^{\circ}$ to South-West, then $45^{\circ}$ to South).
- After Turn 2, Reeta is facing South.
Turn 3: $45^{\circ}$ clockwise from South.
- From South, $45^{\circ}$ clockwise is South-West.
- After Turn 3, Reeta is facing South-West.
Turn 4: $135^{\circ}$ anticlockwise from South-West.
- From South-West, $45^{\circ}$ anticlockwise is South.
- From South, $90^{\circ}$ anticlockwise is East ($45^{\circ}$ to South-East, then $45^{\circ}$ to East).
- Total anticlockwise turn: $45^{\circ} + 90^{\circ} = 135^{\circ}$.
- After Turn 4, Reeta is facing East.
Alternative Method: Calculating Net Displacement Angle
We can also find the final direction by calculating the net effect of all turns.
- Total clockwise turns: $135^{\circ} + 45^{\circ} = 180^{\circ}$ clockwise.
- Total anticlockwise turns: $90^{\circ} + 135^{\circ} = 225^{\circ}$ anticlockwise.
Net turn = Total Anticlockwise turns - Total Clockwise turns
Net turn = $225^{\circ}$ (Anticlockwise) - $180^{\circ}$ (Clockwise) = $45^{\circ}$ (Anticlockwise)
So, from her initial direction (South-East), Reeta makes a net turn of $45^{\circ}$ anticlockwise.
- Starting from South-East, a $45^{\circ}$ anticlockwise turn leads to East.
Both methods confirm that Reeta is finally facing East.
Summary of Turns
| Step | Turn | Direction After Turn |
|---|---|---|
| Initial | - | South-East |
| 1 | $135^{\circ}$ Clockwise | West |
| 2 | $90^{\circ}$ Anticlockwise | South |
| 3 | $45^{\circ}$ Clockwise | South-West |
| 4 | $135^{\circ}$ Anticlockwise | East |
Final Direction
After completing all the turns, Reeta is facing East.
Revision Table: Key Concepts for Direction Problems
| Concept | Explanation | Angle |
|---|---|---|
| Cardinal Directions | North, South, East, West | $90^{\circ}$ apart |
| Intercardinal Directions | North-East, South-East, South-West, North-West | $90^{\circ}$ apart |
| Between Cardinal & Intercardinal | e.g., North and North-East | $45^{\circ}$ apart |
| Clockwise Turn | Movement in the same direction as clock hands | |
| Anticlockwise Turn | Movement opposite to clock hands |
Additional Information on Direction Reasoning
Direction reasoning questions often involve sequences of turns or movements. It's crucial to correctly identify the starting direction and the type and magnitude of each turn. Visualizing the directions on a compass rose can be very helpful. Remember that a full circle is $360^{\circ}$. Turning $360^{\circ}$ clockwise or anticlockwise brings you back to the original direction. A $180^{\circ}$ turn results in facing the opposite direction.
Important Questions from Direction and Distance
- Vijendra walks a certain distance, say X metres, from his home towards the west. Then he turns left and walks 23 metres. After that, he turns left and walks 36 metres. Then he turns left again to walk 23 metres. He finally turns left and walks 18 metres to reach his home. Find the value of X.
Gaurav exits from the backdoor of his north-facing house and walks 25 m straight, then he takes a left turn and walks 36 m, then he turns left and walks 47 m. He turns left again and walks 36 m. How far and in which direction is he from his house now?
Sahasra started running from her house towards the north. After 40 meters she turned left and ran for 75 meters. She then turned right and ran for 30 meters, and again turned right to run 75 meters. In which direction was she running finally?
At the time of sunset, Lopa and Kritika are sitting facing each other. If the shadow of Lopa falls to the right of Kritika, in which direction is Kritika facing?
Srinija walked 9 km towards the west from her home, then turned towards the south and walked 11 km. Then she walked 13 km towards the east, and finally walked 4 km towards the west. How far is Srinija from her initial position?
