Final answer:
To determine the set of transformations to map rectangle ABCD to rectangle A'B'C'D', we analyzed the effects of reflections and rotations. Option 2, reflecting over the y-axis and rotating 180°, is a likely choice unless more details are given about the positioning of A'B'C'D' relative to ABCD.
Step-by-step explanation:
The question asks about the set of transformations needed to map rectangle ABCD to rectangle A'B'C'D'. To answer this, we can look at the properties of the given transformations in the context of a coordinate system. Here are the options interpreted:
- Reflecting over the x-axis will flip the rectangle vertically (flip in the y direction).
- Reflecting over the y-axis will flip the rectangle horizontally (flip in the x direction).
- Rotating 180° essentially flips the rectangle once around both the x-axis and y-axis without changing its orientation.
- Rotating 90° counterclockwise turns the rectangle a quarter turn in a counterclockwise direction.
Considering these, the correct set of transformations depends on how rectangle A'B'C'D' is positioned relative to ABCD. However, we can eliminate some options based on redundant transformations. For instance, option 1 is redundant as reflecting over both axes is the same as rotating 180°. Therefore, option 2 is correct without unnecessary steps - reflecting over the y-axis and then rotating 180° will create the same final position as two reflections. So, this would be a likely choice unless there are specific details about the placement of A'B'C'D'. Other options would result in A'B'C'D' being in a different orientation relative to ABCD.