1. Translation Symmetry
(Sliding)

2. WARM UP = copy down definitions of vocabulary terms into notes
Transformation is the movement (or ‘mapping’) of all the points of a figure according to a common operation
Translation is a type of transformation that ‘slides’ each point of a figure the same distance and directions to a new location
Pre-Image is the original figure before the transformation
where it started
Often named with letters. ie- triangle ABC
Image is the new figure created from the transformation
where it is after the slide
Named with apostrophe after the letters. ie- triangle A’B’C’ called prime

3. Translation Symmetry
A design has translation symmetry if you can slide the whole design to a position in which it looks exactly the same as it did in its original position.
To describe translation symmetry, you need to specify the distance and direction of the translation.
An arrow can show the slide.

4. Slide the figure to the new location indicated by the arrow.
Interpret the rule from the arrow:
Move Down 3
Move Right 4
Move each point of the triangle down 3 and right 4.
New image after the translation

5. Slide the figure to the new location indicated by the arrow.
How far will you move the pentagon?
Up 1, Right 5
Move each point of the pentagon 1 space up and 5 space right.
New image after the translation

6. Coordinates of new location: (-5, -1), (-4, 2), (-1, -1), & (0, 2).
Move the figure down 3 and left 6. Name the coordinates of the new location.
Down 3
Coordinates of new location:
(-5, -1), (-4, 2), (-1, -1), & (0, 2).
Left 6
New image after the translation

7. Coordinate Rules to Describe the Translation
x controls right and left (x + # moves right
(x - # moves left
y controls up and down y + #) moves up
y - #) moves down
Down 3
(x – 6, y – 3) means translate left 6 and down 3
Left 6
*apply the rule to each vertex
New image after the translation
Coordinates of initial location:
(1, 2), (2, 5), (5, 2), & (6, 5).
(x – 6, y – 3)
Coordinates of new location:
(-5, -1), (-4, 2), (-1, -1), & (0, 2).

9. Equation of new line:
Equation of new line:

10. Reflection Symmetry
Or Line Symmetry

11. 3 Lines of Symmetry Determine if the object has line symmetry.
If so, draw all of the lines of symmetry.
Determine if the object has line symmetry. If so, draw all of the lines of symmetry.
3 Lines of Symmetry

12. 4 lines of symmetry Determine if the object has line symmetry.
If so, draw all of the lines of symmetry.
Determine if the object has line symmetry. If so, draw all of the lines of symmetry.
4 lines of symmetry

13. No lines of symmetry. Determine if the object has line symmetry.
If so, draw all of the lines of symmetry.
Determine if the object has line symmetry. If so, draw all of the lines of symmetry.
No lines of symmetry.

14. WARM UP = copy this into your notes
Reflection = a transformation that ‘flips’ a figure across a reflection line to make a mirror image The image and pre-image will be same size, same shape (congruent) Each point of the figure has to be the same distance from the line of reflection.

15. Line Reflection How do we draw a reflection of this image?
What rules do we use to judge that we did it correctly?
Same size, same shape (congruent)
Each point is the same distance from the line of reflection.
If you draw a line from point A to the new point A (written as A’), it would be perpendicular to the line of reflection.

16. Line Reflection
The new image has the same letters but with an apostrophe after them.
We read A’ as “A prime”
We read B’ as “B prime”
We read C’ as “C prime”

17. (x, -y) rule means reflect over x axis
Coordinates of initial location:
(1, 2), (4, 6), (6, 1)
*apply the rule to each vertex
Coordinates of new location:
(1,-2), (4, -6), (6,-1)

18. (-x,y) rule means reflect over y axis
Coordinates of initial location:
(2, 7), (6, 1), (8,3) , (6, 7)
*apply the rule to each vertex
Coordinates of new location:
(-2,7), (-6,1) (-8,3) (-6,7)

20. Coordinate Rules to Describe the Reflection
*apply the rule to each vertex

21. Rotation Symmetry

22. Rotation around an objects own center point
Rotation Symmetry
Rotation around an objects own center point

23. Rotational Symmetry Rules
A shape has rotational symmetry if it fits onto itself two or more times in one complete turn.
First, determine how many times a figure can land on itself including the full turn.
Then divide 360˚ by that number to get the first rotational degree.
For example, the figure above can be turned and land on itself 4 times.
360˚ ÷ 4 = 90˚.
The rotational degrees are 90˚, 180˚, 270˚ and 360˚.

24. Determine if the shape has rotational symmetry
Determine if the shape has rotational symmetry. If it does, find all of its rotational symmetries.
Yes = 180˚, 360˚

25. Determine if the shape has rotational symmetry
Determine if the shape has rotational symmetry. If it does, find all of its rotational symmetries.
Yes = 120˚, 240˚ & 360˚

26. Determine if the shape has rotational symmetry
Determine if the shape has rotational symmetry. If it does, find all of its rotational symmetries.
No rotational symmetry

27. Determine if the shape has rotational symmetry
Determine if the shape has rotational symmetry. If it does, find all of its rotational symmetries.
Yes = 60˚, 120˚, 180˚, 240˚ 300˚, & 360˚

28. Rotation Around a Point outside of the object
Rotation Symmetry
Rotation Around a Point outside of the object

29. A Rotation is…
A rotation is a transformation that turns a figure around a fixed point called the center of rotation.
A rotation is clockwise if its direction is the same as that of a clock hand.
A rotation in the other direction is called counterclockwise.
A complete rotation is 360˚.

30. Describe the Rotation in 2 ways.
120˚ Counter Clockwise
240˚ Clockwise

31. Describe the Rotation in 2 ways.
55˚ Clockwise
305˚ Counter Clockwise

32. Describe the Rotation in 2 ways.
175˚ Clockwise
185˚ Counter Clockwise

33. Describe the Rotation in 2 ways.
165˚ Counter Clockwise
195˚ Clockwise

34. Estimate the angle and direction of the rotation.
About 85˚ Counter Clockwise

35. Before rotating a figure about the origin on a coordinate grid…
Estimate what quadrant the figure will end up in.
It may help to draw a line from one vertex of the object to the origin.
What quadrant would 90˚ clockwise rotation end up in?
Imagine making a right angle with the line.
It will end up in quadrant 4.
What do you notice about the two triangles?

36. Rotate points A-E 90˚ counterclockwise about the origin.D’
Which quadrant will it end up in?
Write a rule for the pattern relating the coordinates of key points to the coordinates of their image after a 90˚ rotation: (x, y) →
Do any points remain unchanged after this rotation?
Do the flag and its image make a symmetric design? C’ E’ B’
(5, 4)
(6, 6)
(3, 6) A’
(0, 0)
(-4, 2)
(-4, 5)
(-6, 6)
(-6, 3)
(-y, x)

37. Rotate points A-E 180˚ counterclockwise about the origin.
Which quadrant will it end up in?
Write a rule for the pattern relating the coordinates of key points to the coordinates of their image after a 180˚ rotation: (x, y) →
Do any points remain unchanged after this rotation?
Do the flag and its image make a symmetric design?
(5, 4)
(6, 6)
(3, 6)
(0, 0)
(-2, -4)
(-5, -4)
(-6, -6)
(-3, -6) A’ B’ C’ D’ E’
(-x, -y)

38. What effect do rotations have on angles?
When you rotate a figure 180˚, does it matter whether you rotate clockwise or counterclockwise?
Compare E to E’, D to D’, and C to C’. What do you notice about each angle pair?
What effect do rotations have on angles?
What effect do rotations have on side lengths? A’ B’ C’ D’ E’

39. Coordinate Rules to Describe the Reflection

40. Enlargement or Reduction
Dilation
Enlargement or Reduction

41. What is a dilation (in math)?
A type of transformation that changes size of the image.
The image is similar (same shape but different size).
Scale Factor: measures how much larger or smaller the image is.

42. Scale Factors A scale factor greater than 1 causes stretching.
A scale factor less than 1 causes shrinking.
Both are dilations.

43. How to Graph Dilations Graph the given points.
Multiply each coordinate by the given scale factor.
List the new ordered pairs.
Plot the new points.

44. Labsheet 4.1 Dilation with scale factor of 3.
Multiply each “x” by 3 and each “y” by 3.
Graph the new ordered pairs. S’ P’ Q’ R’
Point P Q R S
Original Coordinates
(2, 4)
Coordinates after Dilation
(2, 2)
(5, 2)
(4, 4)
(6, 12)
(6, 6)
(15, 6)
(12, 12)

45. How do you find the scale factor?
Take the second figure’s size and divide it by the first figure’s size. 8 4
4 = 8

46. Find the scale factor for the dilation from the solid figure to the dashed line figure.4 16
1/4
4 = 16

47. Find the scale factor for the dilation from the solid figure to the dashed line figure.18 6 3
18 = 6

48. Find the scale factor for the dilation from the solid figure to the dashed line figure.48 24 2
48 = 24

49. Are the two figures similar?
9 cm
Measure parts of both figures.
How do we use these numbers to determine if the figures are similar?
Find the scale factor.
8 ÷ 24 = 1/3
3 ÷ 9 = 1/3
Since the scale factor is the same for both sets of sides, the figures are similar.
24 cm
3 cm
8 cm