Answer:
- reflection over the line AB
- translation by the vector AA'
Explanation:
You want the sequence of rigid motions that transforms ∆ABC to ∆A'B'C'.
Orientation
The order of vertices ABC is clockwise. The order of vertices A'B'C' is counterclockwise. This indicates a reflection must be one of the parts of the transformation.
It appears that line AB is parallel to line A'B', so reflection over the line AB will be a suitable reflection.
Translation
After reflection over the line AB, points A and A' are still distinct. In order to align them, the reflected figure must be translated by the vector AA'. (This would be true for any line of reflection parallel to AB.
The rigid motions required are those of a "glide reflection", a combination of reflection over a line and translation, in either order. The line must be coincident or parallel with AB.
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Additional comment
Technically, a "glide reflection" involves a translation parallel to the line of reflection. If that definition is used, then the line of reflection must be the one that is halfway between AB and A'B'. Such a reflection will put AB on top of line A'B', so that the translation vector AA' is along line A'B'.
If the "glide" is done first, then the translation will move A to a point A'' such that A''A' has the line of reflection as its perpendicular bisector.
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