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Chapter 12—Graphing 121 Using the Rectangular Coordinate Plane
Topics Covered in this Lesson  Introduction to the Coordinate Plane
 Determining the Coordinates of a Point Located on the Coordinate Plane
 Plotting Points on the Coordinate Plane
 Introduction to the Coordinate Plane Definition A rectangular coordinate plane is a 2dimensional graphing system that allows you to specify the exact location of a point, lines, and plane figures.  This kind of graph is used for representing the position of points, lines, and plane figures: Points plotted on a coordinate plane.  Lines plotted on a coordinate plane.  Plane figures plotted on a coordinate plane.  The main part of the rectangular coordinate plane are the x axis, the y axis, and the origin. The x (horizontal) axis:  Is horizontal, running straight left and right.
 Is a number line that increases from left to right.
The y (vertical) axis  Is vertical, or perpendicular to the x axis.
 Is a number line that increases from bottom to top.
The origin  Is the point where the x and y axes meet.
 Is the zero point on both of the axes.
  Note Labels x and y for the axes of a coordinate system is quite common, but not mandatory. They could just as well be labeled p and q, i and j, or Dick and Jane. With few exceptions, we use the most common notation, x and y.  Determining the Coordinates of a Point Located on the Coordinate Plane A point on a plane is located in terms of two numbers: the point's xaxis position and its yaxis position. To see how this works, first look at a point that is plotted on the coordinate plane: We can say that the point is located such that its xaxis position is 4 and its yaxis position is 2. But here is a much simpler way to specify that point on the coordinate plane: (4,2) This is called an ordered an ordered pair — a pair of numbers that are always written in a specific order: x position, followed by the y position. The two values are separated by a comma and enclosed in parentheses. (xposition, yposition) Definition Ordered Pair An ordered pair is a set of two values that arranged in a particular, conventional, significant order.   Note: When you begin working with 3dimensional coordinate graphs, you will see that points must be specified as an ordered triplet  (x, y, z).  Example Notice the location of the point on this coordinate plane. If you follow along the x axis, you can see that the point is located at 3. And if you follow along the y axis, the point is located at 4. So for this particular point: x = 3 and y = 4 Or to write it as an ordered pair, we say this point is located at (3,4) on the coordinate plane.   More Examples Examples & Exercises Work on these endless examples and exercises until you can determine the coordinates of points on a plane without error. Plotting Points on the Coordinate Plane Review of Definition A rectangular coordinate plane is a 2dimensional graphing system that allows you to specify the exact location of points, lines, and plane figures. The x axis is the horizontal number line The y axis is the vertical number line The origin Is the point where the x and y axes meet. Is the zero point on both of the axes.  An ordered pair of numbers represents one particular location, or point, on a coordinate plane. So the ordered pair (3,4) means the point is located where x = 3 and y = 4. The following figures show how to plot the coordinate point (3,4). Procedure To plot a point on a coordinate plane: 
Find the location of the value of x on on the horizontal number line (the x axis). 
Find the location of the value of y on the vertical number line (the y axis). 
Plot the point on the plane that corresponds to the locations of the x and y values.  Example Plot the point (8,6) on this graph: Step 1. Locate the x position, 8  Step 2. Locate the y position, 6  Step 3:Plot the point  More Examples Examples & Exercises Work on these endless examples and exercises until you can determine the coordinates of points on a plane without error.
