Midpoint of a Straight Line Segment

Date: 5/7/96 at 16:18:16
From: Greg Williams
Subject: What is the midpoint?

Geometry:  What is the midpoint of this:  (-3,4) (5,-4)?
Use the distance formula.

Thanks a bunch.

Greg Williams of Tallwood High School in Virginia Beach, VA.

Date: 8/27/96 at 15:4:15
From: Doctor Mike
Subject: Re: What is the midpoint?

Hello Mr. Williams,

The midpoint of a straight line segment can always be found by 
averaging the x-coordinates and averaging the y-coordinates.  For
your example you get (1,0).  The distance formula will give you 
sqrt(32) for the distance from each end to (1,0).  It will also give 
you 2*sqrt(32) for the distance between the original 2 points.  That 
pretty much proves the answer.
   
  In general, you can do the same thing with (A,B) , (X,Y) and
  
        /  A+X     B+Y  \  
       (  ----- , -----  )  
        \   2       2   /
  
Hint: you'll have to keep things like (A-X)^2 = (X-A)^2 in mind.
I hope this helps.
  
-Doctor Mike,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/