To determine if a set of ordered pairs has point symmetry with respect to the origin, we need to check if for every point (x, y) in the set, the point (-x, -y) is also in the set. Essentially, this means that if you were to rotate the entire set 180 degrees around the origin, the points would map onto themselves.
For instance, if we take the pairs (1, 2) and (-1, -2), we can see that they satisfy this condition. If (1, 2) is in our set, then (-1, -2) must also be there for the set to exhibit point symmetry around the origin. Other examples could include (3, -4) and (-3, 4).
In contrast, if we had a point like (1, 2) without its symmetric counterpart (-1, -2), this set would lack point symmetry. Review your set of ordered pairs and apply this rule to identify whether it has point symmetry about the origin.