ROTATIONS UNIT 1 – sept. 8

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

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)

Good things!!!!

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

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?

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

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)

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

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

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

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.

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

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?

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?

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

Rotation Degrees Each quadrant represents 90 degrees Think of a circle

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)

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)

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

How to perform rotations https://www.youtube.com/watch?v=fMU2lDrp76E 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

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’

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

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

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?

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

Rotational symmetry Identify if the figure has rotational symmetry. If yes, identify the angle of rotation. 1. 2. 3.

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?

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.