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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.
fig120101.gif (4079 bytes)

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

fig120101.gif (4079 bytes)

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:

  1. Find the location of the value of x on on the horizontal number line (the x axis).

  2. Find the location of the value of y on the vertical number line (the y axis).

  3. 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.

David L. Heiserman, Editor

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All Rights Reserved

Revised: June 06, 2015