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Plotting Points in the Coordinate Plane

Date: 01/16/2004 at 00:49:19
From: Jennifer
Subject: How do I plot the given points in a coordinate plane?

Plot the given points in a coordinate plane:

(3,0), (2,-3), and (-2,-2)

I don't know what this means or how to do it.  Can you help me?



Date: 01/16/2004 at 10:05:54
From: Doctor Edwin
Subject: Re: how do Iplot the givien points  in  a coordinate  plane

Hi, Jennifer. 

The coordinate plane is a flat surface (like a sheet of paper) that
contains infinite points.  Each point has a set of coordinates, which
are two numbers that tell you where the point is in the plane.  The
point of reference for all the others is called the "origin", and it
has coordinates of (0,0).

The first number in the ordered pair is called the "x" coordinate, and
it tells how far left or right the point is in relation to the origin.
The second number is called the "y" coordinate, and it tells how far
up or down the point is in relation to the origin.

Take a piece of graph paper, and draw two straight lines on it that
cross at a right angle.  One should go up and down (the "y-axis") and
one should go right and left (the "x-axis").

On the x-axis, we use positive numbers to mean how far to the right
the point is, and negative numbers to mean how far to the left.  On
the y-axis, we use positive numbers to mean how far up the point is,
and negative numbers to mean how far down the point is.  You can put
numbers on your axes and your coordinate plane will be all ready:

                               + y-axis
                               |
                               + 3
                               |
                               + 2
                               |
                               + 1
               -5 -4 -3 -2 -1  |  1  2  3  4  5
              --+--+--+--+--+--+--+--+--+--+--+--
                              /|             x-axis
                             / +-1
                        origin |
                               +-2
                               |
                               +-3
                               |


So if you wanted to graph the point (4,2), you can start at the origin
(0,0).  Then you'd move right along the x-axis until you reached
positive 4.  Then you'd move up 2 units since the y coordinate is
positive 2.  Mark a little point there and write (4,2) next to it:

                               + y-axis
                               |
                               + 3
                               |
                               + 2         *(4,2)
                               |
                               + 1
               -5 -4 -3 -2 -1  |  1  2  3  4  5
              --+--+--+--+--+--+--+--+--+--+--+--
                               |             x-axis
                               +-1
                               |
                               +-2
                               |
                               +-3
                               |

Did you ever play the board game Battleship?  It's very much the same
thing--in the game there are letters along the y axis and numbers
along the x axis, and when a player calls something like "B-7" you
find the place where the B row meets the 7 column.

Let's try another point, (-3,-1).  From the origin, you move three
lines to the left (x is negative 3), and one line down (y is negative
1).  Mark a little point there and write (-3,-1) next to it:

                               + y-axis
                               |
                               + 3
                               |
                               + 2
                               |
                               + 1
               -5 -4 -3 -2 -1  |  1  2  3  4  5
              --+--+--+--+--+--+--+--+--+--+--+--
                               |             x-axis
                      *(-3,-1) +-1
                               |
                               +-2
                               |
                               +-3
                               |

If you have 0 for a coordinate, that means that you don't move any
distance in that direction, so you will just stay right on the axis. 
In other words, a 0 for x means you will stay on the y-axis since you
won't move left or right from the origin.

Does that help?  Now on a new sheet, draw and label your x-axis and
your y-axis, and graph your three points the same way.

If you're stuck, or you have any questions, write back and I'll try 
my best to help you.

- Doctor Edwin, The Math Forum
  http://mathforum.org/dr.math/ 
Associated Topics:
Middle School Graphing Equations

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