Question

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

Explanation:

Step1: Analyze point - coordinate changes

Original points like $M(-5,4)$ change to $M'(5,4)$. The $y$ - coordinate remains the same and the $x$ - coordinate changes sign.

Step2: Recall reflection rules

Reflection across the $y$ - axis changes the sign of the $x$ - coordinate while keeping the $y$ - coordinate the same. The rule for reflection across the $y$ - axis is $r_{y - axis}(x,y)\to(-x,y)$.

Answer:

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