5.1 Coordinates in Space

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.

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

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

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)

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

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

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.