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### X Line in a 3D Graph

```
Date: 03/10/2001 at 16:22:38
From: jane pfaender
Subject: x, y, z coordinates

Is the x line on a graph, as drawn on a page, vertical or horizontal?

Thank you.
```

```
Date: 03/10/2001 at 18:09:03
From: Doctor Achilles
Subject: Re: x, y, z coordinates

Hi Jane,

Thanks for writing to Dr. Math.

There are two conventional ways to draw a 3D graph on paper.

+y
|
|
|
|
|
|
(-x)---------------|----------------+x
|
|
|
|
|
|
-y

Where +y is the positive direction and -y is the negative direction
for y.

In this graph, z would be positive coming out of the page at you and
negative going into the page. This is often drawn like this:

+y     -z
|     /
|    /
|   /
|  /
| /
|/
(-x)---------------|----------------+x
/|
/ |
/  |
/   |
/    |
/     |
+z    -y

Here the +z is understood to be coming out of the page and the -z is
understood to be going in.

+z     +y
|     /
|    /
|   /
|  /
| /
|/
(-x)---------------|----------------+x
/|
/ |
/  |
/   |
/    |
/     |
-y    -z

In this case, +x is to the right and +z is up.  -y is coming out of
the page at you and +y is going into the page.

These are actually equivalent representations.

To see that they are, try doing this: hold up your right hand with
side. Point your thumb in the +x direction while pointing your fingers
in the +y direction. Your palm will automatically be facing the +z
direction in both systems. (Try it out for both systems.)

Notice that in both of these conventional representations, x is
horizontal. But there are other equivalent representations that don't
have x pointing horizontally. For example:

+x     -z
|     /
|    /
|   /
|  /
| /
|/
+y---------------|----------------(-y)
/|
/ |
/  |
/   |
/    |
/     |
+z    -x

This is just another perspective on the same representation as the two
conventional representations I showed you above. However, in the two
conventional representations that I'm familiar with, x is always
horizontal.

other math topics, please write back.

- Doctor Achilles, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
High School Equations, Graphs, Translations
Middle School Graphing Equations

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