Question

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

Explanation:

Step1: Analyze coordinates of L and L'

Original L(-6,2), reflected L'(6,2). x flips sign, y stays.

Step2: Analyze coordinates of M and M'

Original M(-5,4), reflected M'(5,4). x flips sign, y stays.

Step3: Analyze coordinates of N and N'

Original N(-3,2), reflected N'(3,2). x flips sign, y stays.

Step4: Match to reflection rule

Flipping x-sign with y unchanged is reflection over y-axis: $r_{y-axis}(x,y)→(-x,y)$.

Answer:

A. $r_{y-axis}(x,y)→(-x,y)$