Coordinates of Vertices of a Rectangular Box through 2 points:

The box is sketched below. We can use the diagram to determine the coordinates of the

other vertices. For example, for the top, left, rear vertex, we know that it has the same X and Z coordinates as the top, right, rear vertex. Only its Y coordinate is different, and must be the same as that of the bottom, left, front vertex. Hence the coordinates of this point are (1,6,9). Analyze the rest of the vertices, and when you are ready, check them.

To find the length, L, of the diagonal, we use the 3-dimensional distance formula: