Direction: Study the information given below carefully and answer the questions that follow.
In which direction is point Q with respect to point M?
South-West
Solution Walkthrough
To determine the direction of point Q with respect to point M, we must carefully follow Dibakar's movements and track his position relative to the starting point M.
Dibakar's Movement Steps
Dibakar's journey can be broken down into sequential steps:
- Start at Point M: Dibakar begins his walk at point M.
- First Leg (M to N): He walks 3 meters in the East direction, reaching point N.
- Second Leg (N to O): At point N, he turns right. Since he was moving East, turning right means he now faces South. He walks 6 meters South to reach point O.
- Third Leg (O to P): At point O, he turns right again. Facing South, a right turn means he now faces West. He walks 7 meters West to reach point P.
- Fourth Leg (P to Q): At point P, he turns left. Facing West, a left turn means he now faces South. He walks 3 meters South to reach point Q.
- Subsequent Legs (Q to S): Dibakar continues walking for two more legs (11m East, then 6m North) to reach point S, but these movements do not affect the position of Q relative to M.
Calculating Position of Q relative to M
We can use a coordinate system to precisely track Dibakar's location. Let point M be the origin $(0,0)$. We'll consider the East direction as positive movement along the x-axis and the North direction as positive movement along the y-axis.
Movement Breakdown with Coordinates:
- M to N: Dibakar moves 3m East. The coordinates of N are $(3,0)$.
- N to O: Dibakar moves 6m South (which is negative y direction). The coordinates of O are $(3, 0 - 6) = (3,-6)$.
- O to P: Dibakar moves 7m West (which is negative x direction). The coordinates of P are $(3 - 7, -6) = (-4,-6)$.
- P to Q: Dibakar moves 3m South (negative y direction). The coordinates of Q are $(-4, -6 - 3) = (-4,-9)$.
Net Displacement Analysis:
The final coordinates of point Q relative to the starting point M $(0,0)$ are $(-4,-9)$.
- The displacement along the x-axis is $-4$m. This means point Q is 4 meters West of point M.
- The displacement along the y-axis is $-9$m. This means point Q is 9 meters South of point M.
Directional Conclusion
Since point Q is located 4 meters to the West and 9 meters to the South of point M, its position relative to M is in the South-West direction.
Similar Questions
In which direction is point S with respect to point O?
What is the shortest distance between point N and point S?
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?
