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A parallelepiped S has base points A ,B ...

A parallelepiped `S` has base points `A ,B ,Ca n dD` and upper face points `A^(prime),B^(prime),C^(prime),a n dD '` . The parallelepiped is compressed by upper face `A ' B ' C ' D '` to form a new parallepiped `T` having upper face points `A",B",C"a n dD"` . The volume of parallelepiped `T` is 90 percent of the volume of parallelepiped `Sdot` Prove that the locus of `A"` is a plane.

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To prove that the locus of point A'' is a plane, we will follow these steps: ### Step 1: Define the Parallelepiped S Let the base points of the parallelepiped S be defined as: - A = (x1, y1, z1) - B = (x2, y2, z2) - C = (x3, y3, z3) - D = (x4, y4, z4) ...
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