Hello everyone, I'm fairly new to maths and have only recently been interested many years after my education so I'm attempting to teach myself fundamentals and things I find interesting. As of that I apologise if this problem is terribly worded

So I have 2 quads, ABCD and A'B'C'D', I know a point P inside ABCD and I want to find a point P' inside A'B'C'D' based on the relationship between the two quads?

For example in this diagram...

I can see from looking that the difference between the 2 based on the order of the verts is a reflection as shown by the blue line, I can then work out P'. However given a different ordering of the second quads verts is there some way to work out what the process is to convert P to P'?

Basically looking for an algorithm that can know what you have to do to P to get P' using only the co-ordinates of the 2 quads.

I hope this makes some sense, having a hard time explaining what I'm trying to do in maths terminology

Many thanks in advance to anyone that can point me in the appropriate direction