Problem #7

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

A reflection across the x-axis

A reflection across the y-axis

A 90° clockwise rotation about the origin

A 180° clockwise rotation about the origin

1 answer

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.