Final answer:
The set of points that satisfy x = 4 and z = 7 forms a vertical line passing through the point (4, 7) in the xz-plane.
Step-by-step explanation:
The geometric description of the set of points whose coordinates satisfy the given conditions x = 4 and z = 7 is a vertical line passing through the point (4, 7) in the xz-plane. This is because the value of x is fixed at 4 and the value of z is fixed at 7, while the value of y can vary. Therefore, all points on this line have an x-coordinate of 4 and a z-coordinate of 7, but the y-coordinate can be any real number.