How to prove this isomorphism-related graph problem is NP-complete? Consider the following problem:  Given two graphs $G_1 = (V_1, E_1)$ and $G_2 = (V_2, E_2)$ and some non-negative integer $k \in \mathbb{N}$, is it possible to delete at most $k$ vertices from $G_1$ to obtain $G_1'$ such that $G_1' \cong G_2$, i.e. the resulting graph is isomorphic to $G_2$.

I have to show that this problem is NP-complete.

Can somebody help me with this problem? It is school homework and I don't know how to solve it.
Here's a hint:  Consider Vertex Cover, which is NP-complete.  If $G = (V,E)$ has a vertex cover of size $k$, then you can remove $k$ vertices from $G$ to obtain $G'$ such that $G'$ is an edgeless graph on $n-k$ vertices.

Edit:  The correct reduction (by using Vertex Cover) shows the problem to be NP-hard.  Given the correct witnesses, you can easily show that it is in NP.