Mapping from three to two dimensions

Question

Mapping from 3-dimensional space (x,y,z) to 2-dimensional space (x',y') is given by the mapping functions: x'=x/z, y'=y/z. Map the square ABCD to the quadrilateral A'B'C'D', where the coordinates of the square are:

A(p,-p,p),

B(p,-p,2p),

C(2p,-p,2p)

and D(2p,-p,p).

What type of quadrilateral is generated by the mapping and what are the coordinates of the four vertices, A', B', C' and D'?

Answer 1

The coordinates of the four points can be calculated as follows: