Using the given diagram, we want to find the coordinates of the vertices of the 3D box. Coordinates in 3D are written as (x, y, z). The x- and y-axes are related in the same way they usually are. However, now we have the added dimension of moving "away from" the paper, in the z-direction. We are told that P is at (6, -3, 9).
Finding A
Notice that point A is at the origin, so the coordinate is (0,0,0).
Finding B
Point B is 6 units along the x-axis but does not move up or down in the y- or z-directions, so the coordinate is (6,0,0).
Finding D
Point D is 3 units in the negative direction on the y-axis. It does not move left or right in the x-direction and it does not move up or down in the z-direction, so the coordinate is (0,-3,0).
Finding C
Point C has the same x-coordinate as point B and the same y-coordinate as D. It also does not move up or down in the z-direction. This means that the coordinate for C is (6, -3, 0).
Finding E
Point E is 9 units up on the z-axis but does not move in the x- or y-directions, so the coordinate is (0,0,9).
Finding F
Point F has the same x-coordinate as B and the same z-coordinate as E. It does not move in either direction along the y-axis. This means that the coordinate for C is (6, 0, 9).
Finding G
Point G has the same y-coordinate as D and the same z-coordinate as E. It does not move in either direction along the x-axis. This means that the coordinate for C is (0, -3, 9).
