Day 13 Isometries.notebook
November 23, 2015
ISOMETRY ­ a transformation that
preserves distance
A transformation is said to preserve distance if the distance between any two given points is the same after the points are transformed.
Example: A'B' is the image of AB
after it is reflected in line p.
A
B
p
A'
B'
Since the length of AB is the same as
A'B', distance is preserved.
If distance is preserved then the following are also preserved:
angle measure
parallelism
midpoint
area
collinearity
Which transformation(s) are isometries?
Which transformation(s) are not
isometries?
Day 13 Isometries.notebook
November 23, 2015
Two kinds of isometries:
Direct: orientation is preserved
Opposite: orientation is not preserved
Orientation of a figure:
A
A
B
C
clock-wise
B
C
counter clock-wise
Day 13 Isometries.notebook
November 23, 2015
Translation
A
B
C
A'
B'
C'
Day 13 Isometries.notebook
November 23, 2015
Rotation
A'
B
B'
C'
A
C
Line Reflection
A
A'
B
B'
C
C'
Day 13 Isometries.notebook
November 23, 2015
Point Reflection
A
C'
B
B'
C
A'
Glide Reflection:
A
C
Slide and Flip
Translation and Reflection
B
A'
B'
C'
Day 13 Isometries.notebook
November 23, 2015
Summary
Transformation
Isometry Direct/Opposite
Line Reflection
Point Reflection
Translation
Rotation
Dilation
NO!!
1. Which transformation is not an isometry?
[A] T3,6 [B] ry=x [C] R0,90° [D] D2
2. Which transformation is a direct isometry?
[A] D−2 [B] T2,5 [C] D2 [D] ry−axis
3. Which transformation is an opposite isometry?
[A] line reflection [B] rotation of 90°
[C] translation [D] dilation
Opposite
Direct
Direct
Direct
N/A
Day 13 Isometries.notebook
4. Which transformation is an example of an
opposite isometry?
[A] (x,y) (x + 3,y ­ 6)
[B] (x,y) (3x,3y)
[C] (x,y) (y,x) [D] (x,y) (y,­x)
5. Which transformation does not preserve
orientation?
[A] dilation
[B] reflection in the y­axis
[C] translation [D] rotation
November 23, 2015