1. LESSON 108 Introduction to Coordinate Space

2. Three-dimensional coordinate system The space is divided into 8 regions by the: x-axis y-axis z-axis Coordinate points are ordered triples (x, y, z) We draw them as an isometric perspective

3. Right-Hand Rule (“Thumb’s Up”) Your index finger is the positive x-axis Your arm is the positive y-axis Your thumb is the positive z-axis

4. Coordinate Planes The three coordinate axes determine the three coordinate planes The xy-plane contains the x- and y-axes. The yz-plane contains the y- and z-axes. The xz-plane contains the x- and z-axes.

5. Octants These three coordinate planes divide space into 8 parts, called octants The first octant, in the foreground, is determined by the positive axes

6. 3-D COORDINATE SYSTEMS Having some difficulty visualizing diagrams of 3- D figures? Then try standing in the corner. The bottom corner of a room is called the origin The wall on your left is in the xz-plane. The wall on your right is in the yz-plane. The floor is in the xy- plane

7. 3-D COORDINATE SYSTEMS The x-axis runs along the intersection of the floor and the left wall. The y-axis runs along that of the floor and the right wall. The z-axis runs up from the floor toward the ceiling along the intersection of the two walls.

8. 3-D COORDINATE SYSTEMS You are situated in the first octant Can you now imagine seven other rooms situated in the other seven octants? There are three on the same floor and four on the floor below They are all connected by the common corner point O

9. Graph the triples (-4, 3, -5) & (3, -2, -6)

10. Finding collinear points

11. Determine if 3 points are collinear

12. Questions? When identifying coordinates, pay attention to other points in the same plane