Final answer:
The transformation represented by the rule (x, y) → (-y, x) is a rotation of 90 degrees counterclockwise about the origin.
Step-by-step explanation:
The transformation represented by the rule (x, y) → (-y, x) is a rotation of 90 degrees counterclockwise about the origin.
To visualize this transformation, consider a point (x, y) in the coordinate plane. The rule states that the x-coordinate becomes the opposite of the y-coordinate, and the y-coordinate becomes the x-coordinate. So, if we apply this rule to a point (1, 2), we get (-2, 1). This means that the point (1, 2) is rotated 90 degrees counterclockwise to (-2, 1).
Similarly, if we apply the rule to another point (-3, 4), we get (-4, -3). So, the point (-3, 4) is also rotated 90 degrees counterclockwise to (-4, -3).