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## Main Question or Discussion Point

If I have a plane with four corner 3-D (x,y,z).. et ceteraa in a coordinate system, how do I translate and rotate it to a new coordinate system orthogonal to it. In other words, do I use the equations/matrices involving sines and cosines to translate the plane?

For instance...

I am not sure if I am doing this right, but do I add a fourth axis (x,y,z,w) and use a matrix to rotate it and transform it? Thank you.

For instance...

I am not sure if I am doing this right, but do I add a fourth axis (x,y,z,w) and use a matrix to rotate it and transform it? Thank you.