Final answer:
The transformation that correctly represents a reflection over the line y=3 is option (b), (x, 6-y). This converts the y-coordinate correctly, such that points above and below y=3 are mirrored appropriately.
Step-by-step explanation:
The student's question is about finding the coordinates of the vertices after a reflection over the line y=3. To reflect a point over this line, you must identify how far the original point's y-coordinate is from y=3 and then move the point the same distance to the other side of the line.
- For option (a), (x, y-6), this implies the point has been moved 6 units downward from its original position, not reflected over y=3.
- Option (b), (x, 6-y), appears to represent a reflection over y=3. If y were equal to 3, then the new y-coordinate would be 6-3=3, meaning the point has not moved, which is correct. If y were greater than 3, then 6-y would be less than 3, and vice versa, exactly how reflection across y=3 would act.
- Option (c), (x, y+6), would move the vertex 6 units upwards rather than reflecting across y=3.
- Option (d), (x, -6+y), is similarly moving the point vertically and does not represent a reflection over the line y=3.
Therefore, the correct transformation that represents a reflection over the line y=3 is option (b), (x, 6-y).