The point is reflected first over the vertical line , and then its image is reflected over the horizontal line . What are the final coordinates of the twice-reflected point?
Options
A
B
C
D
Answer & Analysis
Answer
A
Analysis
Question Analysis:
This problem involves two sequential reflections:
1. First, a reflection over the vertical line (which affects the -coordinate).
2. Second, a reflection over the horizontal line (which affects the -coordinate).
The key is to apply each reflection step by step without combining them prematurely.
Key Concept Explanation:
- Reflection over a vertical line :
- The -coordinate changes based on the rule:
- The -coordinate remains the same.
- Reflection over a horizontal line :
- The -coordinate changes based on the rule:
- The -coordinate remains the same.
Step-by-Step Solution:
1. First Reflection (Over )
- Original point: .
- Reflection line: .
- New -coordinate:
- First reflected point: .
2. Second Reflection (Over
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