The composition transformation involves combining multiple transformations, such as translations, rotations, reflections, or dilations. In your example, \( (x+2, y-4) \) represents a translation transformation.
To define a rule for this transformation:
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Identify the transformations: In the given transformation \( (x + 2, y - 4) \):
- The x-coordinate is increased by 2.
- The y-coordinate is decreased by 4.
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Writing the transformation rule: The general form for a point \( (x, y) \) transforming to a new point \( (x', y') \) can be described as:
- \( x' = x + 2 \)
- \( y' = y - 4 \)
Therefore, the full transformation can be written as:
\[ (x, y) \rightarrow (x + 2, y - 4) \]
This indicates that for any point \( (x, y) \), applying the transformation will yield the new point \( (x + 2, y - 4) \).
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