Which set of ordered pairs has point symmetry with respect to the origin (0, 0)? (5, 4), (-5, 4) (5, 4), (-5, -4) (5, 4), (5, -4) (5, 4), (4, 5)
To determine which 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 coincides with another point in the set.
Let's analyze each set of ordered pairs:
1. (5, 4), (-5, 4):
- The reflection of (5, 4) across the origin is (-5, -4), which does not coincide with any point in the set.
- The reflection of (-5, 4) across the origin is (5, -4), which also does not coincide with any point in the set.
Thus, this set does not have point symmetry with respect to the origin.
2. (5, 4), (-5, -4):
- The reflection of (5, 4) across the origin is (-5, -4), which is the same as the second point in the set.
- The reflection of (-5, -4) across the origin is (5, 4), which is the same as the first point in the set.
Therefore, this set has point symmetry with respect to the origin.
3. (5, 4), (5, -4):
- The reflection of (5, 4) across the origin is (-5, -4), which is not in the set.
- The reflection of (5, -4) across the origin is (-5, 4), which is also not in the set.
Thus, this set does not have point symmetry with respect to the origin.
4. (5, 4), (4, 5):
- The reflection of (5, 4) across the origin is (-5, -4), which is not in the set.
- The reflection of (4, 5) across the origin is (-4, -5), which is also not in the set.
Therefore, this set does not have point symmetry with respect to the origin.
Based on this analysis, the set of ordered pairs that has point symmetry with respect to the origin is (5, 4), (-5, -4).