What does the Cartesian coordinate system consist of?

What does the Cartesian coordinate system consist of?

• A. Two parallel lines
• B. Two perpendicular axes
• C. One horizontal and one vertical line
• D. Three dimensions

Answer: (B)

The Cartesian coordinate system is defined by the presence of two perpendicular axes: the x-axis (horizontal) and the y-axis (vertical). This arrangement allows for the precise plotting of points in a two-dimensional space using ordered pairs (x,y). The orthogonal relationship between the axes is crucial because it establishes a framework for locating points based on their distance from each axis. This system provides a clear way to describe the position of points and to perform mathematical operations involving vectors, slopes, and distances in a two-dimensional plane. It also lays the groundwork for extending these concepts into three-dimensional space with the addition of a z-axis. In contrast, other options do not accurately describe the Cartesian coordinate system. For example, two parallel lines would not create a point of reference for plotting, and while a one-dimensional line can be represented, it does not capture the full structure of the Cartesian system. Similarly, three-dimensional space involves an additional axis and is not part of the basic definition of the two-dimensional Cartesian plane.

The Cartesian coordinate system is defined by the presence of two perpendicular axes: the x-axis (horizontal) and the y-axis (vertical). This arrangement allows for the precise plotting of points in a two-dimensional space using ordered pairs (x,y). The orthogonal relationship between the axes is crucial because it establishes a framework for locating points based on their distance from each axis.

This system provides a clear way to describe the position of points and to perform mathematical operations involving vectors, slopes, and distances in a two-dimensional plane. It also lays the groundwork for extending these concepts into three-dimensional space with the addition of a z-axis.

In contrast, other options do not accurately describe the Cartesian coordinate system. For example, two parallel lines would not create a point of reference for plotting, and while a one-dimensional line can be represented, it does not capture the full structure of the Cartesian system. Similarly, three-dimensional space involves an additional axis and is not part of the basic definition of the two-dimensional Cartesian plane.