Question

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

Explanation:

To determine the transformation, we analyze the rule \((x,y)\to(-x,y)\).

• Translation: Involves shifting the figure (e.g., \((x,y)\to(x + a,y + b)\) with \(a,b

eq0\)), but here \(x\) is negated, not shifted. So not translation.

• Rotation: Rotations (e.g., 90° rotation: \((x,y)\to(-y,x)\)) have different coordinate changes. The given rule doesn’t match rotation patterns.
• Reflection: Reflecting over the \(y\)-axis has the rule \((x,y)\to(-x,y)\), which matches the given transformation.
• Dilation: Involves scaling (e.g., \((x,y)\to(kx,ky)\) with \(k

eq1\)), but here \(x\) is negated, not scaled. So not dilation.

Answer:

Reflection