Finding points of rectangular box in R3
The faces of a rectangular box are parallel to the coordinate planes. Two of the vertices are at the points (1,2,3) and (7,5,4).
*Draw the box and label the vertices
Since it said the faces of the box are parallel to the coordinate planes, I tried finding 2 more vertices parallel to the z-axis. I said the point (1,2,3) on the other side of the z-axis = (1,-2,3) (red) since all y points are negative there and used the same reasoning for the point (7,5,4) (blue). However if I try to join the points (1,2,3), (1, -2, 3), (7,5,4) and (7,-5,4) together, I dont get a rectangular face on the z-axis (yellow). The orange and green line shows how I drew the points (7,-5,4) and (1,-2,3) respectively.
What have I done wrong?