The Math Forum

Ask Dr. Math - Questions and Answers from our Archives
Associated Topics || Dr. Math Home || Search Dr. Math

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!   
Associated Topics:
High School Coordinate Plane Geometry
High School Geometry

Search the Dr. Math Library:

Find items containing (put spaces between keywords):
Click only once for faster results:

[ Choose "whole words" when searching for a word like age.]

all keywords, in any order at least one, that exact phrase
parts of words whole words

Submit your own question to Dr. Math

[Privacy Policy] [Terms of Use]

Math Forum Home || Math Library || Quick Reference || Math Forum Search

Ask Dr. MathTM
© 1994- The Math Forum at NCTM. All rights reserved.