What type of transformation has the same effect as each composition of transformations?

1. Translation [tex](x,y) \rightarrow (x+4,y)[/tex] followed by a reflection across the line [tex]y=-4[/tex]

2. Translation [tex](x,y) \rightarrow (x+4,y+8)[/tex] followed by [tex](x,y) \rightarrow (x-2,y+9)[/tex]

3. Reflection across the line [tex]y=7[/tex], and then across the line [tex]y=3[/tex]

4. Reflection across the line [tex]y=x[/tex], and then across the line [tex]y=2x+5[/tex]

Note: These are all separate problems, not one.

The transformations can be simplified to a single type: the first is a glide reflection; the second is a translation; the third is a translation; and the fourth is a rotation. ;

Answered by JulianneMoore | 2024-06-18

The compositions of transformations yield the following results: a glide reflection for the first sequence, a single translation for the second, another translation for the third, and a rotation for the fourth. Each transformation affects the object differently based on their properties and relationships. By analyzing the transformations step-by-step, we can clarify their overall effects.
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Answered by JulianneMoore | 2024-10-01