Carson constructed a cube, for a class demonstration, so that three of the sides were aligned along the x, y, and z axes of a 3-dimensional graph. He then used stick-on labels to show the ordered triple coordinate for each vertex on the cube and to label the x, y, and z-axes. Unfortunately, before he could present the cube in class, he dropped it and all but three of the labels came off. A picture of the cube with the three remaining labels is below, Assume that the cube sits on a flat surface and plane BCHG is the bottom surface of the cube. D A F (1, 1, 1) E (0, 1,1) B (1, 0, 0) Carson asks you to help him re-label the cube so he can use it in his presentation. He asks you the following three questions. Answer each question correctly, Provide a two or three sentence reason for each answer. Each reason must justify the answer that is given. 1. There are twelve edges on the cube. These edges are line segments such A B or CH. Which edge should be correctly labeled as being along the x-axis? Justify your answer. 2. What are the coordinates of point A? Justify your answer. 3. Which vertex would have the coordinates (0, 0, 1)