The transformation rule \((x, y) \rightarrow (-x, -y)\) describes a reflection through the origin in the coordinate grid. This means that every point \((x, y)\) is mapped to its opposite point in all four quadrants.
For example:
- The point (1, 1) would be transformed to (-1, -1).
- The point (2, -3) would be transformed to (-2, 3).
This transformation also has the effect of rotating the figure 180 degrees around the origin. Thus, one can describe it as a combination of reflection and rotation. However, the simplest and most direct description of the transformation is that it reflects points through the origin.