Question

Create the rule for the composition transformation. example (x+2,y-4)

Answer 1

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:

1. **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.

2. **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 \( (x + 2, y - 4) \).