Question

what is the rule for the reflection?
options:

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

(image shows a coordinate grid with two triangles: top triangle with vertices m(-5,4), n(-2,3), l(-4,2); bottom triangle with vertices m(-5,-4), n(-2,-3), l(-4,-2))

Explanation:

Step1: Analyze Coordinates

Original points: \( M(-5,4) \), \( N(-2,3) \), \( L(-4,2) \). Reflected points: \( M(-5,-4) \), \( N(-2,-3) \), \( L(-4,-2) \).

Step2: Identify Reflection Rule

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

Answer:

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