Rotation or Reflection?

Question

Today, I was asked to "Name and describe each transformation. State whether or not each is an isometry."

The first one I was given was this.

I am now terribly confused over whether it is a rotation or a reflection. The curved arrow suggests it is a rotation, but I suppose it could also be trying to tell me it is reflected. I am very confused, and would like to know what you guys think. Also could someone please explain to me how to know which transformation is being used, as I have several other problems that have more than one possible transformation (Or some that seem like they had multiple transformations used on them).

Any words of wisdom are appreciated. Thanks!

Answer 1

There is no rotation mapping the quadrilateral $ABCD$ to $EFGH$. Indeed such a rotation would have to map $B$ to $F$ and $A$ to $G$ to preserve angles, but then the rest of the quadrilateral would end up above the line $FG$ instead of below it. On the other hand there is a reflection (about the line $x=1$) which does it.

Having said that, the question is ambiguous because the following affine transformation also maps $ABCD$ to $EFGH$: $$ (x,y)\mapsto(2-x,11/3+2x/3-y). $$

Answer 2

The curved arrow simply means the picture on the left has become this after a change(rotation or reflection.)

Imagine that the shape (a trapezium here) is a piece of wood placed on a table. And you are viewing it from directly above the table. Rotation can be carried out without lifting it off the table. Reflection means you lift it off flip it and place it back.

Now comparing both the pictures you can decide which transformation was carried out?