Direction: Study the information given below carefully and answer the questions that follow.
In which direction is point S with respect to point O?
North-East
This problem requires us to determine the final direction of point S relative to the starting point O after a series of movements. We need to carefully track the path taken.
Mapping Dibakar's Walking Path
Let's break down the movements step by step:
- Dibakar starts at point M.
- Walks 3m East to point N.
- From N, turns Right (South) and walks 6m to point O.
- From O, turns Right (West) and walks 7m to point P.
- From P, turns Left (South) and walks 3m to point Q.
- From Q, turns Left (East) and walks 11m to point R.
- From R, turns Left (North) and walks 6m to point S.
Calculating Position of S Relative to O
We can use a coordinate system to find the exact position of S relative to O. Let's assume point M is at the origin (0, 0). We will consider East as the positive x-axis and North as the positive y-axis.
- Point M: (0, 0)
- Point N: Dibakar walks 3m East from M. So, N is at (0 + 3, 0) = (3, 0).
- Point O: Dibakar turns Right (South) from N and walks 6m. South corresponds to the negative y-direction. So, O is at (3, 0 - 6) = (3, -6).
- Point P: Dibakar turns Right (West) from O and walks 7m. West corresponds to the negative x-direction. So, P is at (3 - 7, -6) = (-4, -6).
- Point Q: Dibakar turns Left (South) from P and walks 3m. South is the negative y-direction. So, Q is at (-4, -6 - 3) = (-4, -9).
- Point R: Dibakar turns Left (East) from Q and walks 11m. East is the positive x-direction. So, R is at (-4 + 11, -9) = (7, -9).
- Point S: Dibakar turns Left (North) from R and walks 6m. North is the positive y-direction. So, S is at (7, -9 + 6) = (7, -3).
Directional Analysis from O to S
Now we need to find the direction of point S (7, -3) with respect to point O (3, -6).
- East-West Displacement: We look at the change in the x-coordinates. The difference is $x_S - x_O = 7 - 3 = +4$. A positive value means the displacement is towards the East. So, S is 4m East of O.
- North-South Displacement: We look at the change in the y-coordinates. The difference is $y_S - y_O = -3 - (-6) = -3 + 6 = +3$. A positive value means the displacement is towards the North. So, S is 3m North of O.
Since point S is located 4m to the East and 3m to the North of point O, the direction of S with respect to O is North-East.
Final Conclusion
Based on the coordinate calculations and directional analysis, point S lies in the North-East direction from point O.
Similar Questions
What is the shortest distance between point N and point S?
In which direction is point Q with respect to point M?
What is the distance between points B and H?
What is the direction of point E from point A?
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?
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?
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?
