Quadrants
Quadrants are sometimes used to show the general location of points. As shown in the figure below, the upper right hand region is referred to as Quadrant I or the first quadrant, the upper left hand region is referred to as Quadrant II or the second quadrant, and so forth.
Example 11. Using the figure above, determine in what quadrant the point (-5,3) is located?
Answer:
II (2nd quadrant)
Example 12. In what quadrant is the point (5,-4) located?
Answer:
IV (fourth quadrant)
Example 13. In what quadrant is the point (0,3) located?
Answer:
None. Points on the axes are not in any quadrant. They are between quadrants.
Example 14. In what quadrant is the point (-7,0) located?
Answer:
None. See the previous example.
Each of the coordinate axes may be named by a letter. The most commonly used letter for the horizontal axis is the letter X, and the most commonly used letter for the vertical axis is the letter Y. The axes are then drawn as shown on the following coordinate system:
We now call the horizontal axis the x-axis and the vertical axis the y-axis. However, other letters are used in various applications. Once the axes are labeled as shown, the first coordinate of a point is called the x-coordinate and the second coordinate is called the y-coordinate. Using this system for the point (7,2), the x-coordinate is 7 and the y-coordinate is 2.