Math Help - Help: move point relative to movement of 3 points

Hi. I don't know if this is the right forum, but I need help quick with a problem.

Let's say you have 3 points in 3D-space. p1, p2, p3.
They make up a plane. Then you have another 3D point, p4, relative to this plane. p4 can be placed anywhere, outside or inside the plane.

Then, the 3 points making up the plane moves to q1, q2, q3. I want to calculate q4. That is, p4 moving relative to the 3 points and the plane.

The angle should be maintained relatively. It's ok if the distance is scaled if the distance between the 3 points are scaled somehow.

How do I calculate this?

PLEASE HELP!

Ok let's make it simpler: Just maintain all the distances to the 3 points and put the forth point on the same side of the plane relative to the planes normal.