Final answer:
After applying a 180° rotation and a reflection over the x-axis, the coordinates of △A'B'C' are (3, 9), (4, -3), and (-4, -3), which corresponds to Option D.
Step-by-step explanation:
To determine the coordinates of △A'B'C' after a 180° rotation about the origin followed by a reflection over the x-axis, we need to apply two transformations to the coordinates of △ABC. The coordinates given in the options are assumed to represent the original coordinates of △ABC.
A 180° rotation about the origin will change the sign of both the x- and y-coordinates of each point. So if (x, y) are the original coordinates, after the rotation the new coordinates will be (-x, -y). Next, reflecting these new points over the x-axis will change the sign of the y-coordinates but leave the x-coordinates unchanged. Therefore, the final coordinates would be (-x, y).
Applying these transformations:
- A(-3, 9) becomes A'(3, -9) after rotation and A'(3, 9) after reflection over the x-axis.
- B(-4, -3) becomes B'(4, 3) after rotation and B'(4, -3) after reflection over the x-axis.
- C(4, -3) becomes C'(-4, 3) after rotation and C'(-4, -3) after reflection over the x-axis.
So the correct answer is Option D: (3, 9), (4, -3), (-4, -3).