Lesson 8-8

Example 1
The vertices of a rectangular prism are given by A(4, 4, -4), B(4, -4, -4), C(4, -4, 2), D(4, 4, 2), E(-6, -4, 2), F(-6, 4, 2), G(-6, 4, -4), and H(-6, -4, -4). Represent these vertices in a vertex matrix.  Then graph the rectangular prism.

The vertex matrix for the prism is .

	

Example 2
Bob needs to translate a prism using the vector  = 2, 2, 0. The vertices of the prism have the following coordinates.

A(3, 2, -2)	B(0, 0, -3)	C(-1, 4, -3)

D(-1, 4, 4)	E(3, 2, 4)	F(0, 0, 4)

a.	Write a matrix that will have such an effect on the figure.

b.	Find the coordinates of the vertices of the translated image.

a.	To translate the prism by the vector  = 2, 2, 0, we must first add 2 to each of the x- and y- coordinates. The z-coordinates remain the same.  The translation matrix can be written as
.

b.	Write the vertices of the prism in a 6  3 matrix.  Then add it to the translation matrix to find the vertices of the translated image.

	Original Matrix	+	Translation Matrix	=	Translated Image Matrix
		+		=	

Example 3
Let M represent the vertex matrix of the rectangular prism in Example 1.

a.	Find TM if T = .
b.	Graph the resulting image.

c.	Describe the transformation represented by matrix T.

a.	First find TM.

	TM =   
	TM = 

b.	Then graph the points represented by the resulting matrix.

c.	The transformation matrix T reflects the image of each vertex over the xy-plane.  This results in a reflection of the prism when the new vertices are connected by segments.