LESSON 108 Introduction to Coordinate Space Threedimensional coordinate

LESSON 108 Introduction to Coordinate Space

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

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

Coordinate Planes The three coordinate axes determine 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.

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

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 xzplane. • The wall on your right is in the yzplane. • The floor is in the xy-plane

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.

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

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

Finding collinear points • •

Determine if 3 points are collinear • •

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