Question

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

Explanation:

Step1: Observe the reflection

The pre - image and image are symmetric about the x - axis.

Step2: Recall reflection rule

For a reflection over the x - axis, the x - coordinate remains the same and the y - coordinate changes sign. The rule is $(x,y)\to(x, - y)$.

Answer:

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