Coordinates in the Cartesian Plane

Date: 01/21/2005 at 11:22:40
From: Aaron
Subject: I need help on my math.

How do I get the coordinates for a point on a graph?

Date: 01/21/2005 at 20:06:39
From: Doctor Peterson
Subject: Re: I need help on my math.

Hi, Aaron.

Suppose we are shown a graph with a point A marked on it:

  |
 6+
  |
 5+
  |
 4+           *A
  |
 3+
  |
 2+
  |
 1+
  |
  +---+---+---+---+---+---+--
  0   1   2   3   4   5   6

You draw a vertical line down to the x-axis (the horizontal axis) and
see what number you meet there; that is the x-coordinate of the point:

  |
 6+
  |
 5+
  |
 4+           *A (3,_)
  |           |
 3+           |
  |           |
 2+           |
  |           |
 1+           |
  |           |
  +---+---+---+---+---+---+--
  0   1   2   3   4   5   6

Then you draw a horizontal line to the y-axis (the vertical axis), and
that number is the y-coordinate of the point:

  |
 6+
  |
 5+
  |
 4+-----------*A (3,4)
  |           |
 3+           |
  |           |
 2+           |
  |           |
 1+           |
  |           |
  +---+---+---+---+---+---+--
  0   1   2   3   4   5   6

To avoid confusion, we always give the coordinates with x followed by
y, or (x,y).  Therefore, this point is called (3,4), because its
x-coordinate is 3 and its y-coordinate is 4. You get to it from the
origin, which has coordinates of (0,0), by going right 3 units and up
4 units.

If you have any further questions, feel free to write back.


- Doctor Peterson, The Math Forum
  http://mathforum.org/dr.math/