Triangle ABC is shown on this coordinate grid. △ABC is rotated 180 degrees clockwise about the origin to form △DEF. What conjecture can be made about the relationship between the coordinates of the vertices of the original shape and the coordinates of the vertices of the image of the shape when it is rotated 180 degrees clockwise about the origin?

You must demonstrate that the conjecture is always true or that there is at least one example in which the conjecture is not true.