QQuestionMathematics
QuestionMathematics
What is the rule for the reflection?
\begin{aligned}
& \bigcirc r_{y \text {-axis }}(x, y) \rightarrow(-x, y) \\
& \bigcirc r_{y \text {-axis }}(x, y) \rightarrow(x,-y) \\
& \bigcirc r_{x \text {-axis }}(x, y) \rightarrow(-x, y) \\
& \bigcirc r_{x \text {-axis }}(x, y) \rightarrow(x,-y)
\end{aligned}
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Answer
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Step 1:Let's solve this step by step:
Step 2:: Understand the Reflection Rules
The problem presents four possible reflection rules for points $(x,y)$:
- Reflection over y-axis:
Step 3:r_{y \text{-axis}}(x,y) \rightarrow(-x,y)
2. $$r_{y \text{-axis}}(x,y) \rightarrow(x,-y)
- Reflection over x-axis:
Step 4:r_{x \text{-axis}}(x,y) \rightarrow(-x,y)
2. $$r_{x \text{-axis}}(x,y) \rightarrow(x,-y)
Step 5:: Analyze Reflection Over Y-Axis
- This means the correct rule for y-axis reflection is: $$r_{y \text{-axis}}(x,y) \rightarrow(-x,y)
- When reflecting over the y-axis, the x-coordinate changes sign - The y-coordinate remains the same
Step 6:: Analyze Reflection Over X-Axis
- This means the correct rule for x-axis reflection is: $$r_{x \text{-axis}}(x,y) \rightarrow(x,-y)
- When reflecting over the x-axis, the y-coordinate changes sign - The x-coordinate remains the same
Final Answer
- Reflection over y-axis: r_{y \text{-axis}}(x,y) \rightarrow(-x,y) - Reflection over x-axis: r_{x \text{-axis}}(x,y) \rightarrow(x,-y)
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