plane is textured with an image

I have a polygon primitive plane with 4 subdivisions and this plane is textured with an image. when I select and move one of the edges on the plane the texture distorts as I move the edge. Is there anyway to have the texture hold its shape and not distort even when I move one of the faces or edges on the plane?

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You would need new UVs (texture coordinates), and they are not always easy to make.
You could project the texture, it’s not free, but it is easy to do, the manual has a example:

Easier (and possibly less overhead) than texture projection is simply automatic texture coordinate generation using MWorldPosition or something like that. You can set that up in Blender as well if you use a hg version of YABEE by setting the texture coordinates to ‘GLOBAL’.