The two-dimensional coordinate plane contains the variables x and y and their axes.

The three-dimensional coordinate plane contains the variables x, y, and z and their axes as seen on a following slide.

The coordinate axes determine three all passing through the origin.

The xy-plane, which contains the x- and y-axes and is perpendicular to the z-axis.

  The yz-plane, which contains the y- and z-

axes and is perpendicular to the x-axis.  The xz-plane, which contains the x- and z-

axes and is perpendicular to the y-axis.  

coordinate planes

x

y

z

xy-plane

xz-plane

yz-plane

These coordinate planes separate space into eight regions, called .

Points in the three-dimensional coordinate plane are written as

  These ordered triplets are written in the form

.

For each point, we can draw a rectangular box, which we can call a coordinate box of the point.

octants

orderedtriples

(x,y,z)

For example, the point P has coordinates . So, to plot the point we move 3 units in the positive x direction, 4 units in the positive y direction and 5 units in the positive z direction. The coordinate box can be drawn from there.

Plotted Point Coordinate Box

We can also name the coordinates of the remaining points of the coordinate box.

Questions 1-8: State the coordinates of the point.

1. A

1. B

1. C

2. D

1. E

1. F

1. G

2. H

To plot a point in the 3-D plane, draw the coordinate box using the coordinates of the point to go in the correct direction and then label the point.

Questions 1-3: Sketch a coordinate system in space. In the diagram, show the coordinate box of the given point. Make a new graph for each listed point. Make sure to label the axes.

 1.

2.

3.

4,−2,3( )

−3,5,−2( )

2,−1,5( )