Final answer:
To determine the vertices after a rotation, apply the rotation rules to each vertex. For a 180-degree rotation around the origin, each point (x, y) transforms to (-x, -y), which results in Option D being the correct set of vertices.
Step-by-step explanation:
The task is to determine the vertices of the image after a rotation. To find the vertices after a rotation, we must apply the rules of rotation to each vertex. The correct option that represents the vertices after a rotation about the origin by 180 degrees is Option D, which lists the vertices as: D(-4, 3), E(1, 2), and F(-3, -3). In a 180-degree rotation, each point (x, y) is transformed to (-x, -y). Therefore, applying this rule to the original points given in the question:
- Point D(4, -3) becomes D(-4, 3)
- Point E(-1, -2) becomes E(1, 2)
- Point F(3, 3) becomes F(-3, -3)
These transformed points match the coordinates given in Option D. Hence, Option D is correct.