I want to draw a line(curved) as finger moves on screen after that move a instantited gameobject/rigidbody following that path. 2D

My game is in 2D. Line can be any random line or curve. (have a start and end point) I read that touch need to be converted from 2D screen to 3D world point using the function ScreentoWorldPoint function. Is this necessary because my line have constant Z axis. I want object to follow the path only after the user lifts up the finger (smthg OntouchEXit). Is it necessary to save the path? or can make one object follow the other after a while. How to go about this..