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:

1. Start at Point M: Dibakar begins his walk at point M.
2. First Leg (M to N): He walks 3 meters in the East direction, reaching point N.
3. 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.
4. 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.
5. 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.
6. 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.