How may I extrapolate a point from a rigid 3d body?

Hello, I have x,y,z data for four fixed points on a rigid body i.e:

   Tx        Ty       Tz
A 97.352  -120.289 -958.28
B 109.696 -144.125 -945.219
C 155.972 -118.524 -929.248
D 125.658 -101.497 -949.232

where each row is the coordinate for the different markers on the rigid body (see picture)

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I would like to extrapolate the point alone the vector between A and C x-cm from C (the tip of the tool that the rigid body is attached to).

I know that extrapolating a linear vector alone A-B does not work as it does not preserve the rotational relations between points A-D on the rigid body. May someone explain how may I preserve the rotation and translation between the rigid points in order to estimate the tip position (as per the following image)

Any advice would be greatly appreciated. Many thanks.