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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:

B
+------------------+
/        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
http://mathforum.org/dr.math/
```
Associated Topics:
Middle School Geometry
Middle School Triangles and Other Polygons
Middle School Two-Dimensional Geometry

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