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This task is primarily about finding the centre of rotation that maps A onto A', B onto B', C onto C', etc.
However, it involves two further ideas:
1. the rotation applies to all points in the plane, of which one, the centre, remains invariant;
2. it is easier to visualise a rotation when the centre is on the object.

The position of point E is not important, though one possible position is two units below B on the object.

One way to find F is by trial and error:
• choose a location for E and for F;
• draw the corresponding points E' and F', making sure the whole zig-zag object (ABCDEF) and the whole zig-zag image (A'B'C'D'E'F') are congruent;
• adjust F so that F and F' coincide.
This can be quite fun and can lead to some surprises (though making sure the object and image are congruent can be challenging).

An extreme trial and error example, where the zig-zag ends up with 9 segments, is shown on the final page: PPS.
However, we start by seeing what the rotation of the visible part of the zig-zag line (ABCD) should look like: NEXT PAGE

FREE:
a high-res pdf file of this new GEOaa-zz task