Final answer:
To rotate a figure 180 degrees around the origin, you can transform each point from (x, y) to (-x, -y), essentially flipping the figure around the origin.
Step-by-step explanation:
To rotate a figure 180 degrees in either the positive or negative direction on a coordinate system, you can essentially perform the same action, as rotating 180 degrees clockwise is the same as rotating 180 degrees counterclockwise. Neither of the options listed (reflecting over the x-axis or y-axis, or rotating 90 degrees in any direction) alone will result in a 180-degree rotation. To achieve a 180-degree rotation, you take any point (x, y) on the figure and transform it to (-x, -y). This step changes the points' positions as if the figure has been flipped around the origin, or you may consider it as rotating the figure half a turn around the origin, both achieving the same result.