Question

determining a rule for a reflection
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: Identify reflection axis

The figure reflects over the x-axis (horizontal line y=0).

Step2: Check coordinate change

Point B(0,2) → B'(0,-2); y-coordinate flips sign, x stays same.

Step3: Match rule

Rule for x-axis reflection: $(x,y)→(x,-y)$.

Answer:

D. $r_{x-axis}(x,y)→(x,-y)$