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)

make sketches to see which are straight lines, and which are bisected by the origin.

To determine which set of ordered pairs has point symmetry with respect to the origin (0, 0), we can apply the definition of point symmetry.

Point symmetry means that when a point is reflected across the origin, its image falls onto itself. In other words, if (x, y) is a point, then (-x, -y) should also be a point in order for it to have point symmetry with respect to the origin.

Let's evaluate each set of ordered pairs using this criterion:

1) (5, 4), (-5, 4):
- When we reflect (5, 4) across the origin, we get (-5, -4).
- However, the second pair (-5, 4) is not symmetrical to (-5, -4).
- Therefore, this set does not have point symmetry with respect to the origin.

2) (5, 4), (-5, -4):
- When we reflect (5, 4) across the origin, we get (-5, -4).
- The second pair (-5, -4) is symmetrical to (-5, -4).
- Therefore, this set has point symmetry with respect to the origin.

3) (5, 4), (5, -4):
- When we reflect (5, 4) across the origin, we get (-5, -4).
- However, the second pair (5, -4) is not symmetrical to (-5, -4).
- Therefore, this set does not have point symmetry with respect to the origin.

4) (5, 4), (4, 5):
- When we reflect (5, 4) across the origin, we get (-5, -4).
- However, the second pair (4, 5) is not symmetrical to (-5, -4).
- Therefore, this set does not have point symmetry with respect to the origin.

Based on the evaluations, only the set (5, 4), (-5, -4) has point symmetry with respect to the origin (0, 0).