Final answer:
A 180° counterclockwise rotation about the origin transforms a point (x, y) to (-x, -y), effectively flipping it over both the x and y axes. This rotation preserves the figure's shape and size but changes its position.
Step-by-step explanation:
The rule for a 180° counterclockwise rotation about the origin in a coordinate plane involves transforming the given point (x, y) to (-x, -y). This means, if you have a point on a graph, and you rotate it 180° counterclockwise about the origin, the new position of the point would be directly opposite to the original point on both the x and y axes. For example, if you have a point A at (3, 4), after a 180° counterclockwise rotation about the origin, it would be at position A' (-3, -4).
This rule is applied in various mathematical contexts, such as algebra, geometry, and is particularly important in understanding transformations and symmetry. When visualizing this rotation, imagine flipping a point over both axes. This is a common type of transformation that preserves the shape and size of the figure but changes its position.