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### 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

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/
```
Associated Topics:
High School Coordinate Plane Geometry
High School Geometry

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