1. A metaphor of this could be spinning something around a central point such as when someone is creating pottery because you are forming something around a central y-axis.
2. The concept of the lathe tool is to take the center point/ line of the object that is 2D and to create the 3D object by spinning on that same axis.
3. (a) The center line acts as a reference or starting point for the eventual 3D plane.
(b) The points plotted have (x,y) coordinates and create a 2D outline by connecting the points with lines.
(c) 2D shape/ points revolve around the center line to create a 3D shape with an additional coordinate (x,y) turns into (x,y,z).
4. The mapping is the series of coordinates that created the 2D object, which eventually turned into the 3D object. Every connection between every data point create the mapping that is the lathe tool.