What are the resultant coordinates of (x, y) when it is reflected through the origin?
(-x, -y)
When reflected through the origin, both the coordinates will change their sign i.e. (x, y) becomes (-x, -y) or (-x, -y) becomes (x, y) depending upon the sign. For an example, if we have, the coordinates (-2, 6) its reflection through the origin gives us (2, -6) as a resultant point.