Unit 1:Unit 1:Transformations, Transformations, Congruence, and SimilarityCongruence, and Similarity

Basic Types of Basic Types of TransformatioTransformatio

ns:ns:Translations

ReflectionsRotations

Quadrant IQuadrant II

Quadrant III

Quadrant IV

x-axis

y-axis

(x,y)

Object to ImageObject to Image(Before) (After)(Before) (After)

Before Transformation:

After Transformation:

(‘ = PRIME)A A’

B B’C C’

Translations…Translations…

AA tran translslation ation ""slslides" an object a fixed ides" an object a fixed distancedistancein a given direction.  The original object and in a given direction.  The original object and its translation have the its translation have the same shape and same shape and sizesize, and they , and they face in the same face in the same directiondirection. Objects that are translated are . Objects that are translated are congruentcongruent..*The word "translate" in Latin means *The word "translate" in Latin means "carried across". "carried across".

Example 1:Translate the object down 2 and right 3 units.

Example 1 Solution:Translate the object down 2 and right 3 units.

Example 2:Translate the object (-3, 4)

Example 2 Solution:Translate the object (-3, 4)

Remember: Translations are SLIDING on a graph!!! The shape doesn’t change at all.Translations are SLIDES!!!

                                                            

                                                 

Reflections…

A A rereflflectionection “ “flflips” an object ips” an object and can be seen in water, in a and can be seen in water, in a mirror, in glass, or in a shiny mirror, in glass, or in a shiny surface.  An object and its surface.  An object and its reflection have the reflection have the same same shape and sizeshape and size, but the , but the figures face in opposite figures face in opposite directionsdirections.  In a mirror, for .  In a mirror, for example, right and left are example, right and left are switched. switched.

The line (where a mirror may be placed) is The line (where a mirror may be placed) is called the called the line of reflectionline of reflection.  The distance .  The distance from a point to the line of reflection is the same from a point to the line of reflection is the same as the distance from the point's image to the as the distance from the point's image to the line of reflection. A reflection can be thought of line of reflection. A reflection can be thought of as a "flipping" of an object over the line of as a "flipping" of an object over the line of reflection. reflection.

The object ABCD is being reflected over the x-axis.

Example 3:Reflect the object over the y-axis.

Example 3 Solution:Reflect the object over the y-axis.

Example 4:Reflect the object over x = 2.

Example 4 Solution:Reflect the object over x = 2.

Rotations…

A A rotation rotation is a transformation that turns a is a transformation that turns a figure about a fixed point called the center of figure about a fixed point called the center of rotation.  An object and its rotation are the rotation.  An object and its rotation are the same shape and sizesame shape and size, but the , but the figures may figures may be turned in different directions.be turned in different directions.

Rotations Graphically…Rotations Graphically…Physically rotate the graph paper

and use the original points – just graphed in the different quadrants.

Rules:Rules:When students complete rotating

the original figure clockwise 90˚, 180˚, and 270˚, you can have them come up with the rules on their own.

If you have time, you can have them use the same figure and rotate counter clockwise and come up with the rules of those too.

Rotation Rules:Rotation Rules:

Clockwise

Counter Clockwise

90˚ (y, -x) (-y, x)180˚

(-x, -y) (-x, -y)

270˚

(-y, x) (y, -x)

Rotate 90° counter clockwise

Rotate 90° counter clockwise

Rotate 90° clockwise

Rotate 90° clockwise