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Which series of transformations will map the pre-image $\triangle ABC$ to the image $\triangle A''B''C''$?

Created for Albert.io. Copyright 2016. All rights reserved.

Reflection across the $x$-axis then a translation according to $(x,y)\rightarrow (x-4,y+2)$.

Reflection across the $y$-axis then a reflection across the line $y=x$.

Rotation $180°$ about the origin then a reflection across the line $x=-2$.

Reflection across the line $y=2$ then a translation according to $(x,y)\rightarrow (x-1,y-2)$.

Reflection across the $y$-axis then reflection across the $x$-axis.