A function that is not contractive with respect to any metric

A function that is not contractive with respect to any metric

I am struggling with this homework question with is related to iterated
function system and fixed point theory. The question is:
Let $\Delta \in R^2$ be a filled non-degenerate triangle with vertices
$A,B,C\in R^2$. Let D be the midpoint of the side $BC$. Now define two
affine transformations by $f_1(ABC)=ABD$ and $f_2(ABC)=CAD$. (We write
$f(PQR)=STU$ to mean f$(P)=S,f(Q)=T,f(R)=U$). Let $\mathcal{F}$ be the
iterated function system $\{\Delta;f_1,f_2\}$. Now we need to show
(1)$f_2$ is not contractive w.r.t any metric (that induces on $\Delta$ the
usual topology)
(2) Prove or provide thoughts that $\mathcal{F}$ possese a unique attractor.
(3) explain how is this consistent with the fact that if $\mathcal{F}$ is
an affine iterated function system on $R^M$ that possesses a unique
attractor, then there is a metric w.r.t which is contractive.
For (1) , I've tried to show there is no fixed point of $f_2$. However,
the picture is like shrinking the original toward somewhere along the line
segment from C to the midpoint of AD and I can't see why there is no fixed
point.
I don't know how to do (2) and (3) either .But for (3), I am suspecting
that we have to invent a metric which makes $f_1Uf_2$ being contractive
with respect to this metric. Any ideas? Thanks for help.