Question

a rectangle undergoes a single transformation. for each rule, indicate the type of transformation that occurred.
(x,y) --> (-y, x)
translation
rotation
reflection
dilation

Explanation:

Step1: Recall transformation rules

Translation moves a figure without rotation/reflection/dilation. Rotation rules: 90° counterclockwise is \((x,y)\to(-y,x)\), 90° clockwise is \((x,y)\to(y,-x)\), 180° is \((x,y)\to(-x,-y)\). Reflection over axes: over \(y\)-axis \((x,y)\to(-x,y)\), over \(x\)-axis \((x,y)\to(x,-y)\). Dilation scales coordinates (e.g., \((kx,ky)\)).

Step2: Match given rule

The rule \((x,y)\to(-y,x)\) matches the 90° counterclockwise rotation rule. It's not translation (no shift), not reflection (doesn't match axis reflections), not dilation (no scaling).

Answer:

Rotation