The transformation given by the rule \((x, y) → (-x, -y)\) can be analyzed as follows:
- The point \((x, y)\) is transformed to \((-x, -y)\), meaning both the x-coordinate and the y-coordinate are negated.
- To understand what this means geometrically, consider the point being moved to a position that is directly opposite its original position relative to the origin.
This transformation corresponds to a \(180^\circ\) rotation about the origin, because rotating a point in the plane \(180^\circ\) around the origin results in the coordinates being negated.
Thus, the correct answer is:
A 180° clockwise rotation about the origin.