1. 5.1 Coordinates in Space

2. Coordinate Planes
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.

3. 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

4. z
yz-plane
xz-plane y
xy-plane x

5. 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
ordered
triples
(x,y,z)

6. For example, the point P has coordinates
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

7. Questions 1-8: State the coordinates of the point.
We can also name the coordinates of the remaining points of the coordinate box.
Questions 1-8: State the coordinates of the point. A B C D E F G H

8. 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.