1. Stand Quietly

2. Students will be able to define and apply translations.
Lesson 2.2 Translations
Students will be able to define and apply translations.

3. Warm-Up #33 (11/29/16)
Find the volume of a cylinder if the diameter is 4 inches and height is 10 inches.
Evaluate 3x – 6y if x=3 and y=3
What is translations?

4. Homework (11/29/16)
Worksheet: Transformational Geometry_Translations page 1-4

5. YouTube: Intro to Transformations

6. Transformations Example: (x, y) ↦ (x+3, y)  RULE (5, 12) ↦ (5+3, 12)
A transformation transforms, or maps, the original point to another point. Transformation uses a combination of operations (+, −, ÷, x)
notation: ↦ “maps to” (it is a rule “arrow notation”)
Example: (x, y) ↦ (x+3, y)  RULE
(5, 12) ↦ (5+3, 12)
( 8, 12) new point

7. Practice Problem (x, y) ↦ (x, y - 2 ) (x, y) ↦ (x - 3, y)
(3, -2)
(x, y) ↦ (x, y - 2 )
(x, y) ↦ (x - 3, y)
(x, y) ↦ (2x, y + 2)
(3, -4)
(0, -2)
(6, 0)

8. YouTube

9. Transformation – a change in the ___________, _________ , or _________ of a figure.
Rigid Transformation – a change in the position of a figure that does not change its _______________ or ________________.
Preimage – the __________ figure in a transformation.
Image – the _____________ figure in a transformation.
Isometry – a transformation in which the original figure and its image are ___________.
Prime – a notation to identify new images being created. It looks like this: A’ or A’’ or A’’’ or A’’’’
size
shape
position
size
shape
original
resulting
congruent

10. Transformations on the Coordinate Plane
Algebra 4-2 Transformations on the Coordinate Plane
Line of
reflection
NOT A RIGID TRANSFOMRATION
NOT AN ISOMETRY
Transformations on the Coordinate Plane
Harbour

11. Translations: (x, y) ( x + 2, y - 3)
You “slide” a shape up, down, right, left or all
the above.
Translation is a rigid transformation. The new image will be congruent (isometry) to the Pre-image.
Notation:
(x, y) ( x + 2, y - 3)

12. Summary of Translations
Add to x
Translates RIGHT
Subtract from x
Translates LEFT
Add to y
Translates UP
Subtract from y
Translates DOWN

13. Describe each transformation.
(x+10, y)
(x–5, y)
(x, y+7)
(x, y–6)
(x+3,y–7)
(x–4,y–5)
(x–8,y+9)
translates right 10
translates left 5
translates up 7
translates down 6
translates right 3
and down 7
translates left 4
and down 5
translates left 8
and up 9

14. translated figure up 3 units
Use the given rule to transform the figure. Then describe the transformation.
Rule: (x, y+3)
Add 3 to the y’s.
Preimage
Image
A (1,3)
A’(1, 6)
B (1,1)
B’(1, 4)
translated figure up 3 units
C (4,1)
C’(4, 4)

15. translated figure right 5 units
Use the given rule to transform the figure. Then describe the transformation.
Rule: (x+5, y)
Add 5 to the x’s.
Preimage
Image
A (-4,3)
A’ (1, 3)
B (-4,1)
B’ (1, 1)
translated figure right 5 units
C (-1,1)
C’ (4, 1)

16. translated figure left 2 units
Use the given rule to transform the figure. Then describe the transformation.
Rule: (x-2, y)
Subtract 2 from x’s
Preimage
Image
A (-3,-2)
A’ (-5, -2)
B (-3,-4)
B’ (-5, -4)
translated figure left 2 units
C (0,-4)
C’ (-2, -4)

17. translated figure down 4 units
Use the given rule to transform the figure. Then describe the transformation.
Rule: (x, y–4)
Subtract 4 from y’s.
Preimage
Image
A (2,1)
A’ (2, -3)
B (2,-1)
B’ (2, -5)
translated figure down 4 units
C (5,-1)
C’ (5, -5)

18. y A A’ B B’ C C’ x Image Transformation (x, y) (x + 5, y + 0)
Pre-image
A (-2, 4)
B (-3, 2)
C (-1, 1)
Image
A’ (3, 4)
B’ (2, 2)
C’ (4, 1)

19. y A A’ B C B’ C’ x Image Transformation (x, y) (x - 3, y + 0)
Pre-image
A (-2, 4)
B (-3, 2)
C (-1, 1)
Image
A’ (-5, 4)
B’ (-6, 2)
C’ (-4, 1)

20. y A B C x A’ B’ C’ Transformation (x, y) (x + 0, y - 5) Pre-image

21. y A’ B’ A C’ B C x Image Transformation (x, y) (x + 0, y + 4)
Pre-image
A (-2, 4)
B (-3, 2)
C (-1, 1)
Image
A’ (-2, 8)
B’ (-3, 6)
C’ (-1, 5)

22. y A B C A’ x B’ C’ Transformation (x, y) (x + 3, y - 4) Pre-image

23. y A’ A B’ B C’ C x Transformation (x, y) (x + 5, y + 2) Pre-image

24. y A B C x A’ B’ C’ Transformation (x, y) (x - 4, y - 5) Pre-image

25. y A’ B’ A C’ B C x Image Transformation (x, y) (x - 2, y + 3)
Pre-image
A (-2, 4)
B (-3, 2)
C (-1, 1)
Image
A’ (-4, 7)
B’ (-5, 5)
C’ (-3, 4)

26. Online Practices https://www. ixl