which set of ordered pairs has point symmetry with respect to the origin (0,0)

1- (-12,5), (-5,12)
2- (-12,5), (12,-5)
3- (-12,5), (-12,-5)
4- (-12,5), (12,5)

pick the pair with

(x,y) and (-x,-y)

To determine if a set of ordered pairs has point symmetry with respect to the origin (0,0), we need to check if the reflection of each point across the origin results in the same set of points.

Let's evaluate each set of ordered pairs:

1- (-12,5), (-5,12)
The reflection of (-12,5) across the origin is (12,-5), which is not in the set. So, this set does not have point symmetry with respect to the origin.

2- (-12,5), (12,-5)
The reflection of (-12,5) across the origin is (12,-5), which is also in the set. The reflection of (12,-5) results in the original point (-12,5). Therefore, this set has point symmetry with respect to the origin.

3- (-12,5), (-12,-5)
The reflection of (-12,5) across the origin is (12,-5), which is not in the set. So, this set does not have point symmetry with respect to the origin.

4- (-12,5), (12,5)
The reflection of (-12,5) across the origin is (12,-5), which is not in the set. So, this set does not have point symmetry with respect to the origin.

Therefore, the set of ordered pairs that has point symmetry with respect to the origin is option 2: (-12,5), (12,-5).