Below I have illustrated my two possible interpretations of a line segment being translated:
Interpretation 1:
Interpretation 2:
In the first interpretation, the plane is completely empty, but we are allowed to "speak into existence" a line segment, which we can then push around. The segment in the final position is made up of the same original points
In the second interpretation, every point is already in existence. We define the line segment to be a certain set of points. When we translate said segment, we don't (can't) move the original points. We merely color in different points at the desired final location.
Which of these interpretations, if any, is correct?
Any help is appreciated!