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Chapter 12—Graphing

12-1 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 2-dimensional 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 x-axis position and its y-axis 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 x-axis position is 4 and its y-axis 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.

(x-position, y-position)

 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 3-dimensional 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 2-dimensional 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.

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