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Distance between Two Points

Date: 08/03/99 at 01:37:26
From: Mike Nazzal
Subject: Distance in a 3d plane

I am trying to find an equation to measure the distance between 2 
points on a 3D plane such as:

     point A = (2,3,-4)
     point B = (-2,8,13)

Thank you.

Date: 08/03/99 at 12:18:51
From: Doctor Peterson
Subject: Re: Distance in a 3d plane

Hi, Mike.

Your question really doesn't involve a plane, just the distance 
between two points. If you graph these two points, you can picture 
each one being at the corner of a box, like this:

             /        x=-2      /|
            /                  / |
           /                  /  +
          /y=3               /  / C          Z
         /                  /  /             |
        /                  /  /              |
       /       x=2        /  /y=8            +---- Y
      +------------------+  /               /
      |       z=13       | /               /
      |                  |/               X
     A        z=-4

Now, how can you find the length of the diagonal from A to B? Try 
using the Pythagorean theorem twice: first to find the length of the 
diagonal from A to C, and then using that to find the length of AB. 
You should be able to see a simple 3D distance formula.

- Doctor Peterson, The Math Forum   
Associated Topics:
Middle School Geometry
Middle School Triangles and Other Polygons
Middle School Two-Dimensional Geometry

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