Question

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

Explanation:

Step1: Identify a vertex coordinate

Take point $A$: $A(-2,1)$

Step2: Find its reflected point $A'$

$A'(2,1)$

Step3: Compare coordinates to find rule

For $(x,y)=(-2,1)$, new $x=-(-2)=2$, $y$ stays 1. This matches reflection over $y$-axis: $(x,y)\to(-x,y)$

Answer:

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