Path length refers to the distance travelled along a specific path between two points. It is a measure of the total length covered during the journey. The statement "Path length does not depend on the coordinate system" means that the distance travelled remains the same regardless of the chosen coordinate system.

Explanation:

Initial point:
The initial point is the starting point of the path. The path length is independent of the initial point because it measures the total distance covered irrespective of where the journey begins. For example, if you walk along a circular path, the distance travelled along the path will be the same regardless of where you start.

Final point:
The final point is the destination or ending point of the path. The path length is also independent of the final point because it measures the total distance covered regardless of where the journey ends. For example, if you travel from point A to point B along a straight path, the distance travelled will be the same whether you stop at point B or continue further.

Path taken:
The path taken refers to the specific route or trajectory followed between the initial and final points. The path length is not dependent on the specific path taken because it measures the total distance covered irrespective of the route chosen. For example, if you walk from point A to point B, whether you take a straight line path or a curved path, the distance travelled will be the same.

Coordinate system:
The coordinate system refers to the mathematical framework used to describe the position of points in space. The path length is independent of the coordinate system because it is a physical measure of the distance covered, which remains constant regardless of how the points are represented mathematically. Whether using Cartesian coordinates, polar coordinates, or any other coordinate system, the distance travelled along a path will be the same.

Conclusion:
In summary, the path length does not depend on the initial point, final point, path taken, or coordinate system. It is a measure of the total distance covered along a specific path and remains constant regardless of these factors. The path length is an intrinsic property of the path itself and is unaffected by external factors.