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A sequence of transformations maps [tex]$\triangle ABC[tex]$[/tex] onto [tex]$[/tex]\triangle A^{\prime \prime} B^{\prime \prime} C^{\prime \prime}[tex]$[/tex]. The type of transformation that maps [tex]$[/tex]\triangle ABC[tex]$[/tex] onto [tex]$[/tex]\triangle A^{\prime} B^{\prime} C^{\prime}[tex]$[/tex] is a $[/tex]\square[tex]$. When [tex]$[/tex]\triangle A^{\prime} B^{\prime} C^{\prime}[tex]$[/tex] is reflected across the line [tex]$[/tex]x=-2[tex]$[/tex] to form [tex]$[/tex]\triangle A^{\prime \prime} B^{\prime \prime} C^{\prime \prime}[tex]$[/tex], vertex $[/tex]\square[tex]$ of [tex]$[/tex]\triangle A^{\prime \prime} B^{\prime \prime} C^{\prime \prime}[tex]$[/tex] will have the same coordinates as [tex]$[/tex]B^{\prime}$[/tex].

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A sequence of transformations maps \(\triangle ABC\) onto \(\triangle A^{\prime \prime} B^{\prime \prime} C^{\prime \prime}\). The type of transformation that maps \(\triangle ABC\) onto \(\triangle A^{\prime} B^{\prime} C^{\prime}\) is a rotation.

When [tex]\(\triangle A^{\prime} B^{\prime} C^{\prime}\)[/tex] is reflected across the line [tex]\(x = -2\)[/tex] to form [tex]\(\triangle A^{\prime \prime} B^{\prime \prime} C^{\prime \prime}\)[/tex], vertex [tex]\(B^{\prime \prime}\)[/tex] of [tex]\(\triangle A^{\prime \prime} B^{\prime \prime} C^{\prime \prime}\)[/tex] will have the same coordinates as [tex]\(B^{\prime}\)[/tex].
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