Question

what is the rule for the reflection?
$i_{x\text{-axis}}(x, y) \to (-x, y)$
$i_{y\text{-axis}}(x, y) \to (-x, y)$
$i_{x\text{-axis}}(x, y) \to (x, -y)$
$i_{y\text{-axis}}(x, y) \to (x, -y)$

Explanation:

Step1: Identify a vertex coordinate

Take point $A(-2, 0)$; its image is $A'(2, 0)$.

Step2: Analyze coordinate change

Compare $(x,y)=(-2,0)$ to $(2,0)$: $x$ becomes $-x$, $y$ stays same.

Step3: Match to reflection rule

This matches reflection over $y$-axis: $r_{y\text{-axis}}(x,y)\to(-x,y)$.

Answer:

$\boldsymbol{r_{y\text{-axis}}(x, y) \to (-x, y)}$