A represents the distance traveled by the dog, a scalar quantity, while B is a vector representing the displacement, which is the shortest path from the initial to the final position with direction. Here option A is correct.
Distance is the total length of the path covered by a moving object, regardless of the direction. It is a scalar quantity, meaning it has only magnitude and no direction. Distance is measured in units of length, such as meters, kilometers, etc.
Displacement is the shortest straight-line distance between the initial and final positions of a moving object, along with the direction. It is a vector quantity, meaning it has both magnitude and direction. Displacement is also measured in units of length, but with a specific direction, such as north, east, etc.
In the diagram, A is the curved line that shows the path of the dog from point P1 to P2. The length of this line is the distance traveled by the dog. B is the arrow that points from P1 to P2. The length and direction of this arrow is the displacement of the dog. Here option A is correct.