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In mathematics, a coordinate system is used to uniquely determine the position of a point or other geometric element in a plane. The most common coordinate system is the Cartesian coordinate system. It consists of two perpendicular lines called axes: the x-axis (horizontal) and the y-axis (vertical).
Each point in this system is described by a pair of numbers \((x, y)\), known as coordinates. These coordinates represent the point's distance from the origin along the x-axis and y-axis.
Selecting points by their coordinates allows for precise and clear descriptions of their location in the plane. This foundation is essential for graphing equations and understanding many areas of mathematics.

The coordinate plane is divided into four sections, called quadrants. These quadrants are created by the intersection of the x-axis and y-axis at the origin (0, 0). Each quadrant has distinct characteristics based on the signs of the coordinates:

• Quadrant I: Both x and y coordinates are positive \((x > 0, y > 0)\).
• Quadrant II: x is negative and y is positive \((x < 0, y > 0)\).
• Quadrant III: Both x and y coordinates are negative \((x < 0, y < 0)\).
• Quadrant IV: x is positive and y is negative \((x > 0, y < 0)\).

Points that lie on the axes do not belong to any quadrant. For example, the point (0, -3) lies on the y-axis. Understanding quadrants helps in identifying the location of any point on the plane.

The axes in a coordinate system are the reference lines used to measure the coordinates of points.
In the Cartesian coordinate system, there are two axes: the x-axis and the y-axis.

• The x-axis is the horizontal line that crosses through the origin.
• The y-axis is the vertical line that also crosses through the origin.

These axes divide the plane into four quadrants and are critical for plotting points. If a point has an x-coordinate of zero, it lies on the y-axis. Similarly, if a point has a y-coordinate of zero, it lies on the x-axis.
For the point (0, -3), the x-coordinate is zero, which places it on the y-axis. The y-coordinate of -3 indicates it is three units below the origin. Understanding how to use axes is important for locating and interpreting points in the coordinate system.