Final answer:
When a figure is rotated 180° around the origin, each point is reflected across the x-axis and y-axis. The new coordinates of point D' can be found by negating the x-coordinate and the y-coordinate of point D. Since the question does not provide the coordinates of point D, none of the given options can be confirmed as the correct answer.
Step-by-step explanation:
When a figure is rotated 180° around the origin, each point is reflected across the x-axis and y-axis. In other words, the x-coordinate of a point becomes its opposite, and the y-coordinate becomes its opposite.
Therefore, to find the new coordinates of point D', we can simply negate the x-coordinate and the y-coordinate of point D.
Point D has coordinates (x, y). Negating the x-coordinate gives us -x, and negating the y-coordinate gives us -y. Therefore, the ordered pair of point D' is (-x, -y).
Since the question does not provide the coordinates of point D, we cannot determine the exact ordered pair of point D'.
Therefore, none of the given options (a), (b), (c), or (d) can be definitively confirmed as the correct answer.