isometries page 15-19. isometry – a transformation in a plane that results in an image that is...

IsometriesPage 15-19

Isometry – A transformation in a plane that results in an image that is congruent to the original object.

Which transformations are isometries?

1. Line reflections

2. Point reflections

3. Translations

4. Rotations

5. Glide Reflection

Dilations are NOT isometries. They do not preserve distance!!

Direct Isometry – An isometry that preserves orientation.

Which transformation are direct isometries?

1. Point reflections

2. Translations

3. Rotations

Point reflection in the origin.

Translation:

Rotation:

Opposite Isometry – An isometry that does not preserve orientation.

Which transformation are opposite isometries?

1. Line reflections

2. Glide reflections

Glide Reflection:

Compositions with Isometries

**An even number of opposite isometries results in a direct isometry

**An odd number of opposite isometries results in an opposite isometry

90,2,3 oRT Direct isometryD D

90,oxy Rr Opposite isometryO D

180,90,2,3 oaxisyo RrRT Opposite isometryD D

90,oxy Rr Direct isometryO D

O D

180,oaxisy Rr

O D

)2,3(

)5,0(

)2,1(

T

S

R

4,2, xyyx

)5,4(' R

)4,7(' S

)1,4(' T

Page 17

Page 18