Which set of ordered pairs has point symmetry with respect to the origin (0, 0)?
(9, 2), (-9, 2)
(9, 2), (-9, -2)
(9, 2), (9, -2)
(9, 2), (2, 9)
To determine whether a set of ordered pairs has point symmetry with respect to the origin, you need to check if each point is reflected across the origin, resulting in another point from the same set of ordered pairs.
Let's analyze each set of ordered pairs:
1. (9, 2), (-9, 2)
To check for point symmetry, we reflect each point across the origin:
(9, 2) -> (-9, -2) [reflection across origin]
However, (-9, -2) is not present in the original set, so this set does not have point symmetry with respect to the origin.
2. (9, 2), (-9, -2)
Let's reflect each point across the origin:
(9, 2) -> (-9, -2) [reflection across origin]
(-9, -2) is present in the original set, so this set does have point symmetry with respect to the origin.
3. (9, 2), (9, -2)
Reflecting each point across the origin:
(9, 2) -> (-9, -2) [reflection across origin]
(9, -2) is not present in the original set, so this set does not have point symmetry with respect to the origin.
4. (9, 2), (2, 9)
Reflecting each point across the origin:
(9, 2) -> (-9, -2) [reflection across origin]
(2, 9) is not present in the original set, so this set does not have point symmetry with respect to the origin.
Only the set of ordered pairs (9, 2), (-9, -2) has point symmetry with respect to the origin (0, 0).
(x,y) is symmetric with (-x,-y)
so, what do you think?