Final answer:
The correct answer is to graph the original polygon rotated by 180 degrees counter-clockwise, which involves changing each vertex coordinate from (x, y) to (-x, -y) and then redrawing the polygon with these new points.
Step-by-step explanation:
The question involves a graphical representation of a geometric transformation, specifically a rotation of a polygon by 180 degrees counter-clockwise. When a figure is rotated 180 degrees around the origin, each point (x, y) on the original figure will have its coordinates changed to (-x, -y) on the image. This reflects the points across both the x-axis and the y-axis. Here's how you would graph the rotated image:
- Take each vertex of the original polygon and invert its coordinates. If the original coordinate is (x, y), the new coordinate will be (-x, -y).
- Plot these new coordinates on the grid.
- Connect the vertices in the same order as the original polygon to complete the image of the rotated polygon.
This rotation does not involve a translation, shearing, or resizing of the figure; it simply changes the position by rotating the entire shape 180 degrees counter-clockwise. Thus, option D, stating the image is rotated 180 degrees counter-clockwise, is correct.