An ant is at the bottom-left corner of a grid (point P) as shown above. It aims to move to the top-right corner of the grid. The ant moves only along the lines marked in the grid such that the current distance to the top-right corner strictly decreases. Which one of the following is part of a possible trajectory of the ant during the movement?
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In problems involving movement along a grid, ensure the path is always directed towards the goal and satisfies any conditions given in the problem, such as strictly decreasing distance.
The ant is required to move in such a way that its distance to the top-right corner strictly decreases. This means that at each step, the ant must move in a direction that brings it closer to the top-right corner.
Looking at the options:
1. Option (A): The ant moves left and then up, but it would be increasing the distance to the top-right corner at some point. So this is not a valid trajectory.
2. Option (B): The ant moves right and then up, but again the movement does not strictly decrease the distance.
3. Option (C): This trajectory involves the ant moving both right and up, gradually getting closer to the top-right corner without increasing the distance at any point. This satisfies the condition of the problem.
4. Option (D): The movement here is not consistent with the requirement, as it seems to loop back to the starting point.
Thus, the correct option is (C), as it represents a valid part of the ant's trajectory where the distance to the top-right corner strictly decreases.
