To determine the standard notation for a point in a three-dimensional Cartesian coordinate system, let's examine each of the provided choices.
1. Choice A: [tex]$x, y, z$[/tex]
- This option lists the coordinates [tex]\( x, y, \)[/tex] and [tex]\( z \)[/tex] without enclosing them in parentheses or using any other standard notation that indicates a point.
2. Choice B: [tex]$(w, x, y)$[/tex]
- This option uses parentheses to enclose the coordinates, which is correct in terms of notation. However, it uses [tex]\( w, x, \)[/tex] and [tex]\( y \)[/tex] as the coordinates, which is non-standard. The standard notation uses [tex]\( x, y, \)[/tex] and [tex]\( z \)[/tex].
3. Choice C: [tex]$(x, y, z)$[/tex]
- This option correctly uses parentheses to enclose the coordinates and lists them as [tex]\( x, y, \)[/tex] and [tex]\( z \)[/tex]. This is indeed the standard way to denote a point in a three-dimensional Cartesian coordinate system.
4. Choice D: [tex]$(x, y, y)$[/tex]
- This option also uses parentheses correctly, but it repeats the [tex]\( y \)[/tex] coordinate instead of having [tex]\( x, y, \)[/tex] and [tex]\( z \)[/tex]. This notation is not standard for a three-dimensional point.
Considering these observations, the correct choice is:
C. [tex]$(x, y, z)$[/tex]
This is the standard notation for representing a point in a three-dimensional Cartesian coordinate system.
