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.
Similar Questions
Two different positions of the same dice with faces K, B, V, M, P, and T are shown below. Select the letter that will be on the face opposite to the one having B.
Select the number from among the given options that can replace the question mark (?) in the following series.
3, 6, 9, 18, 21, ?
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?
- 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.
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?
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?
Shashank walks a certain distance, say X m, towards the west, then turns left and walks 35 m, and then turns right and walks 18 m. From there, he turns left and walks 9 m, and then turns left again and walks 60 m. From there, he turns left and walks 9 m, and then turns left again and walks 12 m. He finally turns right and walks 35 m to reach a point that is exactly 10 m to the east of the starting point. What is the value of X?
A and B start from the same point. A cycles 10 km South, then turns to her right and cycles 9 km. B cycles 2 km North, then turns West and cycles 15 km, then turns to her left and cycles 12 km. Where is B with respect to A now?
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Important Questions from Direction and Distance
Sita took an auto from her home in Andheri (A) to go to her college in Fatehpuri (F). Rather than continuing straight on the direct road to the college that had no turns, the auto driver took a diversion after 10 km and tumed right at Bandra (B) crossing, then at Colaba T- point (C) after 8 km turned left, again after covering 12 km turned left at Dalhousi Building (D) and soon after 8 km turned right at Elphinston point (E) and after covering 4 km reached Fatehpuri (F). Had the auto driver taken the direct route how much less distance would Sita have actually travelled between the starting point and the destination?
Radha walks a distance of 9 m towards the South-East. Then she walks 15 m towards the West. From here, she walks 9 m towards the North-West. Finally she walks 6 m towards the East and stands at the point. How far is she standing from the starting point?
According to the time by Nihaal's watch its half past one and the hour hand is pointing towards the north-east. Assuming that there is no change in Nihaal's position, in which direction would the minute hand point after 30 minutes?
According to the time by Rohan's watch, it is half past 6 and the watch's hands are pointing to the south. In which of the given directions will the minute-hand point AFTER exactly 24 hours?
According to the time by Rick's watch its quarter past eight. If the minute hand points towards the east, towards which direction would the hour hand point?
