A figure was transformed on a coordinate grid using the rule (x, y) → (−x, −y). Which of the following describes this transformation?

1 answer

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.