A pentagon with vertices at (1,1), (2,3), (4,3), (5,1), and (3,0) is transformed to a pentagon with vertices at (1,−1), (2,−3), (4,−3), (5,−1), and (3,0). Which transformation was applied?

Question

A pentagon with vertices at (1,1), (2,3), (4,3), (5,1), and (3,0) is transformed to a pentagon with vertices at (1,−1), (2,−3), (4,−3), (5,−1), and (3,0). Which transformation was applied?  
1 point
Rotation 180 degrees about the origin
Reflection over the x-axis

GPT-4o mini · Answer

To determine the transformation applied to the pentagon, we can compare the original vertices with the transformed vertices:

Original vertex (1,1) transforms to (1,-1)
Original vertex (2,3) transforms to (2,-3)
Original vertex (4,3) transforms to (4,-3)
Original vertex (5,1) transforms to (5,-1)
Original vertex (3,0) remains (3,0)

From this observation, we see that every point with a positive y-coordinate in the original pentagon has been reflected to a corresponding negative y-coordinate in the transformed pentagon, while the x-coordinates remain unchanged.

This is a characteristic of reflection across the x-axis.

Thus, the transformation applied is Reflection over the x-axis.