Hi, I\'m having trouble finding a method that can find points B, D, A\',B\',C\'

Question

Hi, I'm having trouble finding a method that can find points B, D, A',B',C' and D'. Does this method relate to the finding the vector ? Basically I'm really confused on how to start this one off;( Google Earth has a feature that allows you to get a 3D view of prominent buildings in various cities (check out the Eifel tower in Paris, for example). Imagine that you are the person in charge of creating a 3d image of the Cube for Google Earth. For this you need to find 3d coordinates of the comers of the top square A, B,C, D, as well as the coordinates of the points A', B',C', D' at which four edges of the Cube intersect the ground. Here A is supposed to be connected to A' by such an edge (see the left photo) and similarly for B and B', C and C', and D and D'. You are not the first person to attempt finding these coordinates. In fact, the last person who tried just got fired yesterday because ho was not able to do the job. You've just taken over and you are supposed to base your work on your predecessors notes. His notes are a mess, but it is clear that be started by letting the ground coincide with the x, y-plane and that the y-axis is supposed to point West and the x-axis North. It is not clear where exactly the origin of his coordinate system is, but wherever it is, in this coordinate system A = (13.0492,30.9498,9.01115) and C = (1.97687,4.68868,17.3632). You may assume that B and D are at equal height above the ground. Finally, it is also clear that all these numbers are measurements in meters. Off you go! Wait, apart from finding those eight coordinates I would also like you to figure out how long one of the sides of the Cube is; what the lengths of the segments AA', BB', CC, DD' are; what the area of the quadrilateral A', B',C',D' is; and what the volumes of the parts of the Cube above and below the ground are.

Explanation / Answer

since A = (13.0492; 30.9498; 9.01115),C = (1.97687; 4.68868; 17.3632) they are at same height so z cordinate of B and D are equal let it be z another thing A' and C' are projection of A and C on ground i.e their z cordinate is zero so A'= (13.0492; 30.9498; 0),C' = (1.97687; 4.68868; 0) z cordinate is zero because take top view of any item you will see only its projection i.e z=0,which is the same principle employed here as the satellite will see it from and although A and C are not on the same height ,their distance formula can be used to find the values Distance AC=BD we can get one fromula from here similarly AB=BC and AD=CD and also angle between line will be equal,from there we can get two eqn solving all five eqn we can get position of B and D B' and D' will just be putting z=0

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