Math Problem Statement
What is a reflection rule that maps each triangle and its image?
Solution
To solve this reflection problem, we need to identify the line of reflection and the transformation rule that maps one triangle onto the other.
Step-by-Step Solution:
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Identify the line of reflection:
- The line of reflection appears to be the line , as the triangle in blue and the triangle in black are symmetric across this line.
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Determine the reflection rule:
- For a reflection across the line , the coordinates of any point are transformed to .
- Therefore, the reflection rule is .
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Equation of the reflection line:
- The equation of the line is .
Answer:
The reflection rule is: where the equation of line is .
Would you like more details on this problem, or do you have any questions?
Related Questions
- How do you find the line of reflection when given two shapes?
- What are other common reflection rules for different reflection lines?
- How does reflecting over differ from reflecting over ?
- Can the distance between corresponding points help verify a reflection?
- How would this transformation rule change if the line of reflection were horizontal or vertical?
Tip:
When reflecting a point across the line , remember that you simply swap the coordinates of the point.
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Math Problem Analysis
Mathematical Concepts
Geometry
Transformations
Reflections
Formulas
Reflection rule across y = x: (x, y) -> (y, x)
Theorems
Reflection across a line theorem
Suitable Grade Level
Grades 8-10