Coordinates of Endpoint of a Segment

Date: 11/01/2002 at 16:12:35
From: Rachel Brock
Subject: Midpoint

Dear Dr. Math,

I am completely stuck on this question: 

Determine the coordinates of the other endpoint of a segment with an 
endpoint at (1,-1) and a midpoint at (2,5). 

We have learned the midpoint formula, but have yet to learn anything 
like this. Thank you for your time!

Date: 11/01/2002 at 18:35:43
From: Doctor Ian
Subject: Re: Midpoint

Hi Rachel,

Here's one way to think about it. Suppose you're standing on a big
grid at location (1,-1). How would you have to move (how far to the
right? how far up?) to get to (2,5)? 

You could represent it this way:

  (2,5) = (1+a, -1+b)

Now, what if instead, you went to 

  (?,?) = (1+2a, -1+2b) ?

In other words, whatever you did to move from (1,-1) to (2,5), you did
again, but starting at (2,5)?  Wouldn't that make (2,5) the midpoint
of (1,-1) and wherever you ended up?

Does this help?  Write back if you're still confused, or if you have
other questions. 

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

Date: 11/02/2002 at 13:09:50
From: Rachel Brock
Subject: Midpoint

Thank you so much for your help. I completely understand it now.