This document discusses rotations in geometry. It defines a rotation as turning a figure about a fixed center point through a given angle. The rules for rotating figures about the origin by 90, 180, and 270 degrees are presented. Rotation matrices for rotating a point by 90, 180, 270, and 360 degrees are shown. Finally, the document states that a rotation is an isometry according to the Rotation Theorem.

1. 9.4 Rotations January 28, 2013
Bellwork
Please remove your snowflake off the door and take it home.
4. Find the point C on the x­axis so AC + BC is a
minimum for A(2, 5) and B(7, 3).
Jan 28­7:35 AM
HW pg. 602 #4­20 evens 1

2. 9.4 Rotations January 28, 2013
9.4 Rotations
Center of Rotation: figure is turned about a fixed point
Angle of Rotation: rays drawn from center of rotation to
a point and its image
Jan 28­8:00 AM
HW pg. 602 #4­20 evens 2

3. 9.4 Rotations January 28, 2013
Rules for Rotations about the Origin:
90 : (­y,x)
180 : (­x,­y)
270 : (y,­x)
Jan 28­9:03 AM
HW pg. 602 #4­20 evens 3

4. 9.4 Rotations January 28, 2013
Jan 31­7:48 AM
HW pg. 602 #4­20 evens 4

5. 9.4 Rotations January 28, 2013
Rotation Matrices
[1
90 : 0 ­1
0 [ 270 :
[ 0
­1
1
0 [
[ 0
180 : ­1 0
­1 [ [ 0 0 [
360 : 1
1
Jan 28­9:01 AM
HW pg. 602 #4­20 evens 5

6. 9.4 Rotations January 28, 2013
Rotation Theorem: A rotation is an isometry.
Jan 28­10:57 AM
HW pg. 602 #4­20 evens 6

7. 9.4 Rotations January 28, 2013
HW pg. 602 #4­20 evens
Jan 28­12:30 PM
HW pg. 602 #4­20 evens 7