chapter 9 Transformations

Chapter 9 Preview

Transformation:  maps (moves) an initial figure (preimage) onto a final figure (image)

There are 4 types of transformations:

1.  Translation
2.  Reflection
3.  Rotation
4.  Dilation

 

 

 

 

Translation:  sliding a preimage in any direction (without turning it)

 

 

 

Reflection: flipping a preimage over a defined line of reflection.

 

 

 

Rotation:  turning a preimage around a defined point (the point of rotation) a certain number of degrees.

 

 

 

Dilation:  reducing or enlarging a preimage 

 

 

 

Section 9.1  Reflections

Reflection: flipping a preimage over a defined line

             

Line of Reflection:  the defined line the preimage is reflected over (dashed segment above)

 

The reflected image (red) is congruent to the preimage (blue)

 


This results in a congruence transformation or an isometry

 

Line of Symmetry: a line or fold location for a figure that produces halves that match exactly (are congruent)

      

isosceles triangle                rectangle                             square

 

 

Section 9.2  Translations

Translationa transformation that moves (slides) all points of a figure the same distance in the same direction

 

 

 

 

 

Composition:  a transformation made up of successive transformations

 

 

 

 

 

Glide Reflection:  a composition of a translation and a reflection in a line parallel to the direction of the translation

 

 

 

 

Section 9.3  Rotations

Rotation:  a transformation that turns every point of a preimage through a specified angle and direction around a fixed point

                                       

 

 

 

 

Section 9.4  Tessellations