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Line segment JK shown at the right, is reflected over the y-axis to form the line segment J'K'. Rhoda concludes that the y-axis is a perpendicular bisector of KK' and Andy concludes that the lines segments JK and J'K' are parallel. Whose conclusion is correct?

User Mrjohn
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Final answer:

Andy's conclusion that the line segments JK and J'K' are parallel is correct.

Explanation:

Andy's conclusion is accurate because when a point is reflected over the y-axis, its x-coordinate changes sign while the y-coordinate remains the same. In this case, the line segment JK and its reflection J'K' have the same slope but opposite orientations, indicating that they are parallel. Rhoda's conclusion that the y-axis is a perpendicular bisector of KK' is incorrect because the reflection does not necessarily imply that the segments are bisected or perpendicular to each other.

The reflection only results in a change of orientation across the y-axis. Therefore, Andy's observation about the parallelism of JK and J'K' holds true based on the properties of reflections over the y-axis.

When a point undergoes a reflection over the y-axis, the x-coordinate changes sign while the y-coordinate remains unchanged. This transformation preserves the slope of the line segments but reverses their orientation, resulting in parallel lines. Rhoda's assumption about the y-axis being a perpendicular bisector overlooks the fundamental property of reflections. Hence, Andy's conclusion aligns with the geometrical principles governing reflections over the y-axis.

User Goober
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