To find the midpoint of a line segment using paper folding, you need to fold the paper in such a way that the two endpoints of the line segment coincide. This means that when you fold the paper, the two ends of the line segment should lie directly on top of each other. This method ensures that the fold creates two equal lengths on either side of the midpoint. The other options do not achieve this: folding on a specific point does not guarantee that the endpoints overlap, folding perpendicular to the edge of the paper does not align the endpoints, and folding parallel to the line does not create the necessary overlap. Therefore, the correct answer is that the endpoints should lie on each other.