1. Chapter 6
Day 1
What is a
Transformation?

2. Transformers
Have you seen the movie?

3. In the movie… The Chevy Camaro transforms into ______________.
Bumblebee

4. into _________________.
The Semi-Trailer Cab
transforms
into _________________.
Optimus Prime

5. In the dictionary, the word transform means to change.

6. Transformations In geometry, a transformation also means to change.
When a figure moves from one place to another on a coordinate plane a transformation has occurred.
The original figure has changed positions!
original
new

7. There are four basic types of transformations.
Three of the transformations change the position of a shape.
One of the transformations changes the size of a shape. 

8. It is common practice to name shapes using capital letters:
It is common practice to name transformed shapes using the same letters with a
“prime symbol”:
original
image
new
image

9. Now we will look at each type of transformation individually.
Translations
Reflections
Rotations
Dilations

10. 1. Translations
Slide

11. Translations Translation = Slide
A Translation slides each point (or vertex)
of a figure the same distance and in the same
direction.
Nothing changes about the figure except for its position on the
coordinate plane. The image is the same size, the same shape and it’s
pointing in the same direction as the original.

12. Let's examine some translations related to coordinate geometry.
Translations are SLIDES
Let's examine some translations related to coordinate geometry.
The example shows how each vertex moves the same distance in the same direction.
original
image
The translation of an object is called its image. 
Notice in the figure above… 
If the original object was labeled with letters, such as triangle ABC,
the image may be labeled with the same letters followed by a prime symbol, A'B'C'.

13. Translations are SLIDES
What are the coordinates for A, B, C? A (___,___) B (___,___) C (___,___) What are the coordinates for A’, B’, C’? A’ (___,___) B’ (___,___) C’ (___,___) Did the image slide left or right? How many units did the figure slide? Compare the x-coordinate on A and A’. What do you notice?
image
A(-4, 5) B(-1, 1) C(-4, -1)
A’(2, 5) B’(5, 1) C(2, -1)
Slide Right
How many units did the figure slide? slide 6 units
Compare the x-coordinate. It increased by 6.

14. In this example, the "slide" moves the figure 7 units to the left and
Translations are SLIDES
In this example, the "slide"  moves the figure 7 units to the left and
3 units down.

15. 2. Reflection
Flip

16. Reflections Reflection = Flip A reflection flips a figure over a
A reflection flips a figure over a
line called a line of reflection.
A figure and its reflection have the same shape and size, but the figures face in opposite directions-like a mirror image.
In a reflection, something will always be pointing in an opposite direction.
Notice in the picture of the money. The hand on the ground is pointing right.
In the mirror image the hand is pointing left.
Notice on the original figure point A is pointing to the left. A’ is pointing to the right.
Line of reflection.
“It’s the mirror”

17. Reflections are Flips The reflection of an object is called its image.
Notice in the figure below…
If the original object was labeled with letters, such as polygon ABCDE, the image may be labeled with the same letters followed by a
prime symbol, A’ , B’ , C’ ,D’ , E’.

18. Reflections are Flips
Reflections can be seen in water, in a mirror, in glass, or on a shiny surface. 
Same shape and size. Figures face in opposite directions. 
In a mirror, for example, right and left are switched.
mirror
In a reflection, something will always be pointing in an opposite direction.
-Notice in the picture of the money. The hand on the ground is pointing right.
In mirror image the hand is pointing left. Reflection is over the y-axis.
-In the tiger picture notice the ears on the tiger are pointing up towards
the sky. In the reflection the ears are pointing down. Reflection is over the x-axis.
-The mountain peak is point up towards the heavens. In the image the peak
is point down. Reflection is over the x-axis.
-Looking at the children by the pond. I always wondered what they were
doing or looking at. Well anyway, notice the little girl standing up in the
pretty dress. Her cute blond little head is pointing up. In her reflection
her head is points down. Reflection is over the x-axis.
Look at each picture.
Can you find the “line of reflection” (mirror)?
Can you tell the original object from its reflection?
Is the reflection across the x-axis or y-axis?
Do you notice something pointing in an
opposite direction?

19. Reflections are Flips
The line (where a mirror may be placed) is called the line of reflection.  A reflection can be thought of as a "flipping" of an object over the line of reflection.
In this class the line of reflection will either be the x-axis or the y-axis.
over the x-axis
over the y-axis

20. Reflections are Flips What are the coordinates for A, B, C?
What is the line of reflection?
How did the points change
from the original to the reflection?
A(2, -3) B(5, -4) C(2, -4)
A’(2, 3) B(5, 4) C(4, 4)
Line of Reflection--> X-Axis
How did the points change? x-coordinate stayed the same, y-coordinate changed to opposite sign.

21. 3. Rotation
Turn

22. Rotations Rotation = Turn
A rotation is a transformation that turns a figure about a fixed point called the center of rotation.
An object and its rotation are the same shape and size, but the figures are turned in different directions.

23. Rotations are Turns Rotations can occur in either a
clockwise or counter-clockwise direction.
Clockwise
Counter-clockwise
Same direction as the
hands of a clock.
Opposite direction

24. Rotations are Turns
To work with rotations, you need to be able to recognize angles of certain sizes. A clock is a good example that illustrates the different angles we’ll be working with when looking at rotations:
    
Explain each clock in regards to its clockwise rotation.
Rotation from the 12 to the 3 is a 90 degree rotation.
Rotation from the 12 to the 6 is a 180 degree rotation. Hands are straight across from each other.
Rotation from the 12 to the 9 is a 270 degree rotation.
Rotation from the 12 all the way around and back to the 12 is a 360 degree rotation.

25. Rotations are Turns You Try! Write your answer on a piece of paper.
Estimate the degree of each rotation: 90 ̊ , 180 ̊ , 270 ̊
Name the direction of the rotation: clockwise or counter-clockwise
180 degrees, clockwise
270 degrees, clockwise
90 degrees, counter-clockwise

26. 4. Dilations
Size Change

27. Dilations Dilation = Size Change
A dilation is a transformation that produces an image that is the same shape as the original, but is a different size.
A good real-life illustration of dilation would be our pupils and how they react to sunlight.
Our pupils reduce in size (or get smaller) when we are in the sunlight.
Our pupils enlarge in size (or get bigger) when it’s dark.

28. Dilations are Size Changes
A dilation used to create an image larger than the original is called an enlargement.  A dilation used to create an image smaller than the original is called a reduction.
enlargement
enlargement
A scale factor is used to create the
enlarged or reduced image.
reduction
original

31. Stay Puft Attack– Ghostbusters

32. T-Rex Attack – Jurassic Park

33. Hogwarts Castle – Harry Potter

34. Rivendell – Lord of the Rings

35. Metropolis – Superman Returns

36. Remember, dilations always involve a change in size.
Dilations are Size Changes
Remember, dilations always involve a change in size.
                                              
Notice how EVERY coordinate of the original triangle has been multiplied by the scale factor (x2).

37. Almost Done!
Let’s practice…

38. Name the transformation in the picture. Translation Reflection
Rotation
Dilation
Rotation
Clockwise 180 degrees Counter-clockwise 180 degrees
What is the degree of rotation clockwise?
How about counter-clockwise?

39. Is the dilation an enlargement or reduction?
Name the transformation in the picture.
Translation
Reflection
Rotation
Dilation
Dilation - enlargement
Is the dilation an enlargement or reduction?

40. Is the reflection across the x-axis or y-axis?
Name the transformation in the picture.
Translation
Reflection
Rotation
Dilation
Reflection across the x-axis
Is the reflection across the x-axis or y-axis?

41. Name the transformation in the picture. Translation Reflection
Rotation
Dilation
Translation

42. Is the reflection across the x-axis or y-axis?
Name the transformation in the picture.
Translation
Reflection
Rotation
Dilation
Reflection across the y-axis
Is the reflection across the x-axis or y-axis?

43. Dilate ½ Is the dilation an enlargement or reduction?
Name the transformation in the picture.
Translation
Reflection
Rotation
Dilation
Dilate ½
Pre-image
image
Dilation – reduction
Teachers, this may be a good time to point out
the vocabulary pre-image being the original and image being the new copy.
Is the dilation an enlargement
or reduction?

44. Name the transformation in the picture. Translation Reflection
Rotation
Dilation
What is the degree of rotation clockwise?
How about counter-clockwise?
Rotation
Clockwise 90 degrees Counter-clockwise 270 degrees

45. Closure What is a Transformation?
In geometry, a transformation means to change.
When a figure moves from one place to another on a coordinate plane a transformation has occurred.

46. There are four basic types of transformations.
Three of the transformations change the position of a shape.
One of the transformations changes the size of a shape. 

47. End of PowerPoint