Its path must be straight line.
The forces acting on the particles are friction and normal forces from the table and gravitational force from the earth.
The normal force of the table is cancelling the gravitational force of the earth.
Frictional force is acting in the direction opposite to the direction of velocity. So, acceleration due to force is also in the direction opposite to that of velocity.
Since, direction of velocity and acceleration is in same line, thus, the displacement of the body will be in straight line.
Thus, the path must be straight line.