Final answer:
The correct reflection of point A'B'C' across the line y = 2 will be a set of points with the same x-coordinates and new y-coordinates calculated as 4 minus the original y-coordinates. The provided options do not correctly explain this transformation without knowing the specific initial y-coordinates of points A'B'C'.
Step-by-step explanation:
The reflection of point A'B'C' across the line y = 2 will result in the points having new y-coordinates that are the same distance from the line y = 2 as they were before the reflection, but on the opposite side of the line. The x-coordinates will remain unchanged. If a point has a y-coordinate above the line y = 2, after reflection, it will be the same vertical distance below y = 2, and vice versa for points below the line. Mathematically, if a point is at (x, y), then after reflection across the line y = 2, the new point will be at (x, 4 - y). This translates the points vertically across the line y = 2.
Hence, if we apply this to the general coordinates (x, y) of points A'B'C', we get the new coordinates of reflected points A''B''C'' as (x, 4 - y). This makes the given option b) A'B'C' becomes A'B'C'' with coordinates (x, -2) incorrect because it assumes that the new y-coordinate would be -2, which is not correct without knowing the original y-coordinates.