Final Answer:
The correct statements are:
Point F → Point F'
Parallelogram DEFG → Parallelogram G'F'E'D'
Parallelogram DEFG maps to parallelogram D'E'F'G'
Step-by-step explanation:
In a rotation of 90 degrees to the right, each point (x, y) in the original parallelogram DEFG is mapped to a new point (-y, x) in the image parallelogram G'F'E'D'. Let's evaluate each statement:
Point F → Point F'
- Original coordinates of F: (x_F, y_F)
- After a 90-degree rotation: (-y_F, x_F)
- Therefore, point F corresponds to point F'.
Parallelogram DEFG → Parallelogram G'F'E'D'
- The rotation of each point in DEFG corresponds to the mapping described above, resulting in the image parallelogram G'F'E'D'. This includes the rotation of all vertices and sides.
Point D of the pre-image corresponds to point D' of the image.
- For point D, the coordinates (x_D, y_D) become (-y_D, x_D) after the rotation. Thus, point D corresponds to point D'.
ED of the pre-image corresponds to G'F' of the image.
- Original coordinates of E: (x_E, y_E)
- Original coordinates of D: (x_D, y_D)
- The vector ED is given by (x_D - x_E, y_D - y_E)
- After the rotation, the coordinates of G'F' are (-y_D + y_E, x_D - x_E)
- Therefore, ED corresponds to G'F'.
Parallelogram DEFG maps to parallelogram D'E'F'G'
- This statement is correct, as demonstrated in the explanations above.
In summary, all three statements are correct, and the rotations and corresponding mappings align with the properties of a 90-degree rotation to the right.