In a two-dimensional Cartesian coordinate system, a point is represented by a pair of coordinates, \((x, y)\). Here, \(x\) indicates the position of the point along the horizontal axis (the x-axis), and \(y\) indicates the position of the point along the vertical axis (the y-axis).
When extending this concept to a three-dimensional Cartesian coordinate system, an additional coordinate is needed to represent the position of the point along a third axis, the z-axis. This new coordinate system includes three axes:
1. The x-axis, which represents the horizontal dimension.
2. The y-axis, which represents the vertical dimension.
3. The z-axis, which represents the depth dimension (moving in and out of the plane formed by the x and y axes).
To denote a point in this three-dimensional space, we use a triplet of coordinates \((x, y, z)\), where:
- \(x\) represents the position along the x-axis,
- \(y\) represents the position along the y-axis, and
- \(z\) represents the position along the z-axis.
Therefore, the correct way to represent a point in a three-dimensional Cartesian coordinate system is:
B. [tex]\((x, y, z)\)[/tex]
