Question

what is the rule for the reflection?
$r_{x\text{-axis}}(x, y) \to (-x, y)$
$r_{y\text{-axis}}(x, y) \to (-x, y)$
$r_{x\text{-axis}}(x, y) \to (x, -y)$
$r_{y\text{-axis}}(x, y) \to (x, -y)$
graph with points m(-5,4), n(-2,3), l(-4,2), l(-4,-2), n(-2,-3), m(-5,-4)

Explanation:

Step1: Analyze coordinates before and after reflection

Take point \( L(-4, 2) \) and its image \( L'(-4, -2) \), \( M(-5, 4) \) and \( M'(-5, -4) \), \( N(-2, 3) \) and \( N'(-2, -3) \).

Step2: Identify the reflection rule

For each point \((x, y)\), the \( x \)-coordinate remains the same, and the \( y \)-coordinate becomes its opposite. This matches the rule for reflection over the \( x \)-axis: \( r_{x\text{-axis}}(x, y) \to (x, -y) \).

Answer:

\( r_{x\text{-axis}}(x, y) \to (x, -y) \) (the third option)