Modelling our 5 × 5 × 5 Rubik’s cube

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The picture on below shows what you see when you look at the cube from above using Google Earth

Google Earth allows you to view many prominent buildings in 3D. Imagine that you are the maths wiz at Google whose job it is to create a 3D image of our cube for Google Earth. This means that you have to find coordinates of the corners of the square A, B, C, D visible from the top, as well as the coordinates of the points $A' , B' , C' , D'$ at which four edges of the cube intersect the ground. As indicated in the picture on the left, $A$ is supposed to be connected to $A'$ by such an edge, and similarly for $B$ and $B'$ , $C$ and $C '$ , and $D$ and $D'$ .

It is your first day on the job and you are supposed to base your work on that of your predecessor, who got fired yesterday. Their notes are a terrible mess, but it is clear that they started modelling the cube by letting the (flat) ground coincide with the $xy$-plane and having the x-axis point North and the y-axis point West. Their notes don’t tell you where the origin of the coordinate system is supposed to be, but wherever it may be, in this coordinate system we have

$B$ = (2.7997, 22.3302, 11.9406), $B'$ = (1.9651, 19.8699, 0), $D$ = (29.2866, 13.3456, 11.9406).

Your job is to determine the coordinates of the remaining corners of the building ($A, C$) ; the side length of the cube ($A', C', D'$) ; the lengths of the four segments $AA'$ , $BB'$ , $CC'$ , $DD'$.

I have no idea how to go about this question! I missed out on the class where this question was explained! Can someone explain the steps to me please? I tried searching it up but all I found was this explanation but it wasn't clear enough for me

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