How can I scale a set of vertices to the size of another set of vertices?

Question

I have a mesh that is shaped like a frame. Basically I cut a hole in a plane by selecting knife project in edit mode.

Now I would like to animate this mesh with the help of shape keys. I want to take the four inner vertices and scale them up so they are in the exact same position as the outer ones (effectively making the frame disappear). Scaling itself is not the problem but I cannot figure out a way to scale it just the right amount. Unfortunately I can only manipulate the position values individually (in the pane to the right) but not the scaling. Does anyone know of a way to do this?

Any help would be greatly appreciated!

Answer 1

In the begining, create shape keys you'll use for animation (as NoviceInDisguise suggested, thanks):

Then, in Edit mode you select the vertices you'd like to scale. To not mess up pivot center, select only vertices located on one plane. Turn on snap during transform with Shift + Tab, set the Pivot Point to the median with Ctrl+<:

In this case you don't need to remove doubles, and now it's possible to use shape key, created before. In Object mode drag the slider and test how it works: