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A sequence of transformations maps [tex]\( \triangle ABC \)[/tex] onto [tex]\( \triangle A''B''C'' \)[/tex].

1. The type of transformation that maps [tex]\( \triangle ABC \)[/tex] onto [tex]\( \triangle A'B'C' \)[/tex] is a ______.
2. 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 ______ of [tex]\( \triangle A''B''C'' \)[/tex] will have the same coordinates as [tex]\( B' \)[/tex].



Answer :

GinnyAnswer
To explain the sequence of transformations clearly, let's break it down:

1. The first transformation that maps [tex]$\triangle ABC$[/tex] onto [tex]$\triangle A'B'C'$[/tex] could be a translation, rotation, or any other transformation, but the problem doesn't specify which, so we can call it a "transformation" for now.

2. After [tex]$\triangle A'B'C'$[/tex] is formed, it undergoes a reflection across the line [tex]$x = -2$[/tex] to create [tex]$\triangle A''B''C''$[/tex].

Finally, we need to determine which vertex of [tex]$\triangle A''B''C''$[/tex] will have the same coordinates as [tex]$B'$[/tex]. Since [tex]$\triangle A'B'C'$[/tex] is reflected in the line [tex]$x = -2$[/tex], and one vertex keeps the same position, it must be that [tex]$B'$[/tex] was located right on the line [tex]$x = -2$[/tex] to begin with. Thus, its reflection will also be on the line, indicating that [tex]$B''$[/tex] has the same coordinates as [tex]$B'$[/tex].

Therefore, the correct answers are:

1. The type of transformation is a transformation (it could be a specific type like a translation or rotation).
2. The vertex of [tex]$\triangle A''B''C''$[/tex] that will have the same coordinates as [tex]$B'$[/tex] is B''.

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