1. Precalculus
8-8 Transformation Matrices in 3-D Space
You can find the coordinates of each __________________ of a rectangular prism if
given 2 points from opposite corners.
EX1: A(2, 2, -2) and E(-3, -2, 1) are opposite corners of a rectangular prism.
uuu
r
a) Find the vector AE
b) Use the coordinates of the vector to find the coordinates of the other vertices.
B
C
D
F
G
H
c) Write the prism in matrix form.
Remember (chapter 2) that certain matrices can be used to ________________________
(rotate, flip, slide, dilate) a polygon.
Likewise, certain matrices can be used to transform ____________________________.
EX2: You are working on a computer animation project. You need to translate a prism
r
using the vector a = 3, 3, 0 . The vertexes of the prism have the following coordinates:
A(2, 1, -4) B(-1, -1, -4) C(-2, 3, -4)
D(-2, 3, 3) E(2, 1, 3) F(-1, -1, 3)

2. EX3: Let M represent the matrix from Example 1.
 1 0 0 
 
a) Find TM if T =  0 1 0 
 0 0 −1 
 
b) Describe the transformation represented by matrix T.
HW p. 540 (7 – 19 all)