# Math Help - 3d

1. ## 3d

pliz help me to plot the three dimensions accurately by using the graph show it step by step,eg.(-5,4,4)

2. Originally Posted by zasi
pliz help me to plot the three dimensions accurately by using the graph show it step by step,eg.(-5,4,4)
Hello,

I'm not quite certain what you don't understand.

First you need a coordinate-system. You have given a point in 3-D-space. So I assume that you should use a coordinate-system with 3 axes. For convenience I assume the these axes are perpendicular to each other.

Now you have to determine how you want to draw these axes:

i)Put the y- and the z-axis into the drawing plane. Then the x-axis has to be reduced bei a constant faktor. 1/2*√(2) ≈ 0.707 is not a bad choice. Then you can construct a cuboid(?) with the origin and your given point at opposite sides auf a diagonal. (see attachment)

ii)Only the z-axis is in the drawing plane. All axes are scaled equal. Then you have an isometric coordinate-system in which you can very easily construct the cuboid to locate the given point. (see attachment)

EB

3. Hello, zasi!

pliz help me to plot the three dimensions accurately
by using the graph. Show it step by step: e.g. P(-5,4,4)

If you've never done this before, you need to know some basics.

We take our familiar xy-plane and "lay it on the floor".
Then the z-axis will run up and down.

The first "octant" (where all three coordinates are positive) looks like this:
Code:
            z
|
|
|
|
|
|
* - - - - - - - y
/
/
/
/
/
x

It may help the visualization if I draw in the "walls" and "floor".
Code:
            z
* - - - - - - *
/|             |
/ |             |
/  |             |
/   |             |
*    |             |
|    * - - - - - - * y
|   /             /
|  /             /
| /             /
|/             /
*- - - - - - -*
x

I remind you that the z-axis extends below the "floor"
. . (that is where z is negative)
that the y-axis extends to the left of the "left wall",
and the x-axis extends behind the "back wall".

To plot P(-5, 4, 4), note what it says:
. . x = -5, y = 4, z = 4.

Starting at the origin, we move -5 in the x-direction
. . (that's 5 units behind the "back wall"),
then move +4 in the y-direction
. . (that's 4 units to the right),
then move +4 in the z-direction
. . (that's 4 units up).
And there is point P(-5, 4, 4).

It's difficult to draw (or type) a three-dimensional situation
. . on a two-dimensional screen, but I'll try.
Code:
            z           P
|           o
|           :
|           :4
|           :
|   * - - - *
|  /    4
| /-5
|/
* - - - - - - - y
/
/
/
/
/
x

Think of directions to your friend's new apartment.

You start at a mutually-agreed location, say, City Hall.

You are told to drive 5 blocks north,
. . then and 4 blocks east, locating the building,
. . then take the elevator to the fourth floor.
And there is his/her apartment.