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: original $A(-2, 0)$; image $A'(2, 0)$

Step2: Analyze coordinate change

For $A(-2,0)\to A'(2,0)$: $x$-value flips sign, $y$-value stays.

Step3: Match to reflection rule

This matches reflection over $y$-axis: $(x,y)\to(-x,y)$

Answer:

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