1. ROTATIONS
UNIT 1 – sept. 8

2. Do Now a. What is the image after translation of (x,y) (x-2, y+3)?
Write the coordinates.
b. After translating, reflect the image over the line y=x. Write the coordinates.
Today’s Date: 9/8

3. Do Now - Review Starting coordinates
Point S (-7, -5)
Point T (-6, -8)
Point U (2, -5)
First: complete translation (x,y)  (x-2, y+3)
S’ (-9,-2)
T’ (-8, -5)
U’ (0, -2)
Second: complete reflection across line y=x
S’’ (1, -9)
T’’ (-5, -8)
U’’ (-2, 0)

4. Good things!!!!

5. Agenda Objective & Essential Question Translations review
Reflections review
Intro to rotations
Notes
Examples
Rotation activity
Rotational symmetry
Independent practice
Exit Ticket

6. Objective & Essential Questions
SWBAT perform dilations when given a function
SWBAT explain how a dilation is different from other transformations
Essential Questions
How do you rotate a figure in the coordinate plane?
How can you determine rotational symmetry?

7. Agenda Objective & Essential Question Translations review
Reflections review
Intro to rotations
Notes
Examples
Rotation activity
Rotational symmetry
Independent practice
Exit Ticket

8. Translations Practice Point B: (-7, 2) (x,y)  (x+9, y)
A translation is when we move, or slide, a figure
Orientation (direction) does not change
Addition and subtraction
Notation: (x,y)  (x + h, y + a)
Isometric transformation
Practice
Point B: (-7, 2)
(x,y)  (x+9, y)

9. Agenda Objective & Essential Question Translations review
Reflections review
Intro to rotations
Notes
Examples
Rotation activity
Rotational symmetry
Independent practice
Exit Ticket

10. Reflections Reflection over x-axis: (x,y)  (x, -y)
A reflection is when we reflect a figure to have a mirror image
Orientation (direction) flips
Notation: (x,y)  (x, -y)
The negative sign tells us this is a reflection over the x axis
Isometric
Tips
Reflection over x-axis: (x,y)  (x, -y)
Reflection over y-axis: (x,y)  (-x, y)
Reflection over line y = x: (x,y)  (y, x)
Reflection over line y = -x: (x, y)  (-y, -x)
Practice:
Reflect the point (9, 7) over the line y = -x

11. Agenda Objective & Essential Question Translations review
Reflections review
Intro to rotations
Notes
Examples
Rotation activity
Rotational symmetry
Independent practice
Exit Ticket

12. Rotations
A rotation is a transformation that turns a figure about a fixed point, called the center of rotation
The measure of the rotation is called the angle of rotation
ALL ROTATIONS WILL BE COUNTER CLOCKWISE UNLESS OTHERWISE STATED.
Think of rotations as forming a circle around the center of rotation.

13. Rotations
A rotation of _____ degrees places an object back in its original position.
Each quadrant on the coordinate plane represents 90 degrees
360

14. Rotations What is the center of rotation?
How many degrees does the Earth have to travel to get to the opposite side of the sun?

15. Rotations What is the center of rotation?
If you get on the Ferris wheel, how many degrees must you go around before you are back where you started?

16. Rotation degrees 90 degrees: (x , y)  (-y, x)
180 degrees: (x , y)  (-x, -y)
270 degrees: (x , y)  (y, -x)
360 degrees – no change!

17. Rotation Degrees
Each quadrant represents 90 degrees
Think of a circle

18. Guided Practice 180 degrees: (x , y)  (-x, -y)
Rotate point B (2,3)
90 degrees: (x , y)  (-y, x)
90 degrees: (2, 3)  (-3, -2)
180 degrees: (x , y)  (-x, -y)
180 degrees: (2, 3)  (-2, -3)
270 degrees: (x , y)  (y, -x)
270 degrees: (2, 3)  (3, -2)

19. Partner Practice Rotate point F (3, -4) 90 degrees: (x , y)  (-y, x)
180 degrees: (x , y)  (-x, -y)
180 degrees: (3, -4)  (-3, 4)
270 degrees: (x , y)  (y, -x)
270 degrees: (3, -4)  (-4, -3)

20. Agenda Objective & Essential Question Translations review
Reflections review
Intro to rotations
Notes
Examples
Rotation activity
Rotational symmetry
Independent practice
Exit Ticket

21. How to perform rotations
Step 1: Draw figure on graph paper
Step 2: Trace x-axis and y-axis on patty paper
Step 3: Trace figure with patty paper
Step 4: Rotate patty paper COUNTER CLOCKWISE

22. Perform a Rotation
Rotate the rectangle with vertices A(2,1) B(2,-2) C(6,1) D(6,-2) by 90 degrees
Draw the coordinate plane
Draw rectangle ABCD
On patty paper, trace everything – x-axis, y-axis, and rectangle with labeled points
Place point of pen on origin and rotate counterclockwise
Write points A’ B’ C’ D’

23. Agenda Objective & Essential Question Translations review
Reflections review
Intro to rotations
Notes
Examples
Rotation activity
Rotational symmetry
Independent practice
Exit Ticket

24. Rotational Symmetry
A figure has rotational symmetry if you can rotate it 180 degrees (or less) so that its image matches the original figure
The degree measure that the figure rotates is the angle of rotation

25. Angle of Rotation Identify how many lines of symmetry the figure has
Divide 360 by that amount
Why do we use 360 degrees??
What is a line of symmetry??
Does an equilateral triangle have rotational symmetry?

26. Lines of Symmetry The line of symmetry cuts the figure in half
If you draw a line between two points on opposite sides of the reflection, that line will be perpendicular to the line of reflection

27. Rotational symmetry
Identify if the figure has rotational symmetry. If yes, identify the angle of rotation.

28. Exit Ticket
Find the rotation of 90o, 180o, 270o, and 360o of the point (-3, 5) without graphing
What is the angle of rotational symmetry for this figure?

29. Homework Uploaded on class website
You must either print or hand write your responses to turn in
IF you do not have computer or internet access, you must copy down the questions before you leave.