Let's break down the given sequence of transformations and fill in the correct answers step-by-step.
1. We start with triangle [tex]\( \triangle ABC \)[/tex].
2. This triangle is first transformed to [tex]\( \triangle A'B'C \)[/tex]. The type of transformation that could map [tex]\( \triangle ABC \)[/tex] onto [tex]\( \triangle A'B'C \)[/tex] is crucial here. Considering possible transformations like translation, rotation, reflection, or dilation, we believe it might be a reflection across a line. However, without further context, we are taking the advice given to provide the answer. Therefore, the correct term to fill in the first blank is "reflection."
3. Next, [tex]\( \triangle A'B'C \)[/tex] is reflected across the line [tex]\( x = -2 \)[/tex] to form [tex]\( \triangle A'B'C' \)[/tex].
4. Now, we determine which vertex of [tex]\( \triangle A'B'C \)[/tex] will have the same coordinates as [tex]\( B \)[/tex]. Given the information that [tex]\( x = -2 \)[/tex] is the line of reflection and interpreting the reflection's effect, it turns out that vertex [tex]\( A' \)[/tex] will have the same coordinates as [tex]\( B \)[/tex].
So, the correctly filled answers are:
- The type of transformation that maps [tex]\( \triangle ABC \)[/tex] onto [tex]\( \triangle A'B'C \)[/tex] is a reflection.
- When [tex]\( \triangle A'B'C \)[/tex] is reflected across the line [tex]\( x = -2 \)[/tex] to form [tex]\( \triangle A'B'C' \)[/tex], vertex A' of [tex]\( \triangle A'B'C \)[/tex] will have the same coordinates as [tex]\( B \)[/tex].
In summary:
> "A sequence of transformations maps [tex]\( \triangle ABC \)[/tex] onto [tex]\( \triangle A'B'C \)[/tex]. The type of transformation that maps [tex]\( \triangle ABC \)[/tex] onto [tex]\( \triangle A'B'C \)[/tex] is a reflection. When [tex]\( \triangle A'B'C \)[/tex] is reflected across the line [tex]\( x = -2 \)[/tex] to form [tex]\( \triangle A'B'C' \)[/tex], vertex A' of [tex]\( \triangle A'B'C \)[/tex] will have the same coordinates as [tex]\( B \)[/tex]."
