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)
Ans. = B.
A set of ordered pairs has point symmetry with respect to the origin (0, 0) if for every point (x, y) in the set, the point (-x, -y) is also in the set.
Let's examine each set of ordered pairs given:
(5, 4), (-5, 4):
In this set, the point (-5, 4) is not present, so this set does not have point symmetry with respect to the origin.
(5, 4), (-5, -4):
In this set, both (-5, -4) and (-5, 4) are present, satisfying the condition for point symmetry with respect to the origin.
(5, 4), (5, -4):
In this set, both (5, -4) and (-5, 4) are present, satisfying the condition for point symmetry with respect to the origin.
(5, 4), (4, 5):
In this set, neither (4, -5) nor (-4, 5) are present, 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:
(5, 4), (-5, -4)
To determine whether 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 over the origin results in the same set of points.
Let's analyze each set of ordered pairs:
1. (5, 4), (-5, 4)
When we reflect (5, 4) over the origin, we get (-5, -4), which is not in the given set. Therefore, this set does not have point symmetry with respect to the origin.
2. (5, 4), (-5, -4)
When we reflect (5, 4) over the origin, we get (-5, -4), which is in the given set. So the first pair has point symmetry with respect to the origin.
3. (5, 4), (5, -4)
When we reflect (5, 4) over the origin, we get (-5, -4), which is not in the given set. Therefore, this set does not have point symmetry with respect to the origin.
4. (5, 4), (4, 5)
When we reflect (5, 4) over the origin, we get (-5, -4), which is not in the given set. Therefore, 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:
(5, 4), (-5, -4)