8. find the congruence transformation that maps ∆abc to ∆a’b’c’. explain your reasoning

In this case, to flip any of the points to map up accurately to the other points, we would have to do a transformation of reflection about the y-axis. The reason behind this is that out of other transformation process, we can only achieve the image of triangle ∆A’B’C’ through reflection.

Dilation will not work since it only changes the size of the object. The shape and position will not affected.

A translation will not work because although the shape can move, it still needs to flip to achieve triangle ∆A’B’C’.

A rotation will also not work because when you rotate it, the shape will still not map over the new one.

Therefore the only answer to this question would be to reflect triangle ∆ABC about the y-axis.