Advanced Data Interpretation: Background You’ll Need 2

  • Determine the region a point is on a graph

The [latex]x[/latex]-axis and the [latex]y[/latex]-axis form the rectangular coordinate system. These axes divide a plane into four areas, called quadrants. The quadrants are identified by Roman numerals, beginning on the upper right and proceeding counterclockwise. See the image below.

the four quadrants of the rectangular coordinate system

In the rectangular coordinate system, the four quadrants are defined by the intersection of the [latex]x[/latex] (horizontal) and [latex]y[/latex] (vertical) axes, each representing a distinct combination of positive and negative values:

  • Quadrant I (positive [latex]x[/latex] and [latex]y[/latex])
  • Quadrant II (negative [latex]x[/latex], positive [latex]y[/latex])
  • Quadrant III (negative [latex]x[/latex] and [latex]y[/latex])
  • Quadrant IV (positive [latex]x[/latex], negative [latex]y[/latex]).

These quadrants help in categorizing the position and movement of points or graphs in the coordinate plane.

The graph shows the x y-coordinate plane. The x and y-axis each run from -7 to 7. The top-right portion of the plane is labeled I, the top-left portion is labeled II, the bottom-left portion is labeled III, and the bottom-right portion is labeled IV.

When we located where a specific point is on the cartesian coordinate plane we can specify which quadrant that point lies in.

A tricky situation is when one of the coordinates are zero. Where is the point [latex]\left(0,4\right)[/latex] located? Where is the point [latex]\left(-2,0\right)[/latex] located? The point [latex]\left(0,4\right)[/latex] is on the [latex]y[/latex]-axis and the point [latex]\left(-2,0\right)[/latex] is on the [latex]x[/latex]-axis.

Points on the Axes

Points with a [latex]y[/latex]-coordinate equal to [latex]0[/latex] are on the [latex]x[/latex]-axis, and have coordinates [latex]\left(a,0\right)[/latex].

 

Points with an [latex]x[/latex]-coordinate equal to [latex]0[/latex] are on the [latex]y[/latex]-axis, and have coordinates [latex]\left(0,b\right)[/latex].

What is the ordered pair of the point where the axes cross? At that point both coordinates are zero, so its ordered pair is [latex]\left(0,0\right)[/latex] . The point has a special name. It is called the origin.

the origin

The point [latex]\left(0,0\right)[/latex] is called the origin. It is the point where the [latex]x[/latex]-axis and [latex]y[/latex]-axis intersect.