A triangle with vertices , , and is reflected first over the line and then over the line . What are the coordinates of the image of point after these two reflections?
Options
A
B
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D
Answer & Analysis
Answer
A
Analysis
Question Analysis:
This question is about two successive reflections of a point within a triangle over a vertical and a horizontal line.
The main focus is on correctly applying the rules for reflecting points over these types of lines.
Key Concept Explanation:
When reflecting a point over a vertical line , the new -coordinate is , and the -coordinate remains the same.
When reflecting a point over a horizontal line , the new -coordinate is , and the -coordinate remains the same.
Step - by - Step Solution:
1. First, reflect point over the line :
- Using the formula for reflection over a vertical line , with and , we have . The -coordinate stays the same, so the image has coordinates
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