Ordered Pairs vs. Coordinates

Date: 9/9/96 at 10:50:13
From: O'Brien, Thomas, F
Subject: Ordered Pairs vs. Coordinates

Dr. Math,

I was approached today by another teacher to explain to her the
difference between an ordered pair and coordinates. Would you please
answer this question for me? I would like to relay your reply to her. 

Thank you for your help,

Thomas O'Brien

Date: 9/9/96 at 11:25:20
From: Doctor Robert
Subject: Re: Ordered Pairs vs. Coordinates

An ordered pair is just a pair of numbers, usually enclosed in 
parentheses and separated by a comma, in which the order makes a 
difference.  That is, (a,b) is not the same as (b,a). Now, these 
numbers might represent the coordinates of a point in a plane, but 
they also might represent ordered pairs of a function. For example 
(45,60000) might represent a $60000 income at age 45. 

Ordered pairs can represent many different things - components of 
vectors, for example - but coordinates, I believe, should be 
interpreted as representing the x-distance and the y-distance from a 
given origin.

I hope that this helps.

-Doctor Robert,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/