Graphing and Describing Rotations Transformations Day 5 we spent a day focusing on Translations A translation is a slide that moves a figure to a different position left right up or down ID: 761998
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Graphing and Describing “Rotations” TransformationsDay 5
we spent a day focusing on “Translations” A translation is a slide that moves a figure to a different position (left, right, up or down) without changing its size or shape and without flipping or turning it.
A reflection (flip) creates a mirror image of a figure. We spent a day on “Reflections”
Today… We will focus on “Rotations” A rotation (turn) moves a figure around a point. This point can be on the figure or it can be some other point. This point is called the point of rotation . P
1) Translations 2) Reflections 3) Rotations4) DilationsThe first 3 transformations preserve the size and shape of the figure . That means…If your pre-image (the before) is a polygon, your image (the after) is a congruent polygon. If your pre-image contains parallel lines, your image contains congruent parallel lines If your pre-image is an angle, your image is an angle with the same measure. Congruency Could this represent a translation?
Let’s Get Started Section 1: Describing RotationsSection 2: Graphing Rotations 180º
Describing a Rotation When you rotate a figure, you can describe the rotation by… Giving the direction: clockwise or counter-clockwiseGiving the degrees that the figure is rotated around the point of rotation: 90º, 180º, 270º
Describing a Rotation 90º rotations move the figure over 1 quadrant (CW or CCW ) 180º rotations move the figure over 2 quadrants 270º rotations move the figure over 3 quadrants pre-image What are 2 ways to describe the rotation from A to D ? What are 2 ways to describe the rotation from A to C ? What are 2 ways to describe the rotation from A to B ? NOTE: 180º rotations turn the figure upside down !
Turn and Talk Which can be described as a 180º rotation around the origin? Be prepared to share your reasoning with the class. Figure #1 Figure #2 A B A B
Turn and Talk Which describes the rotation of the cell phone? Select ALL that apply. 90° clockwise 180º clockwise 270° clockwise90° counter clockwise 180º counter clockwise270° counter clockwise
You Try #1 Describe the given rotation. Give both the CW and CCW description.
You Try #2 Analyze the given transformation.Which of the following could map the Blue square onto the Green? Reflection across the x-axis. 180º rotation around the origin. A translation 6 left and 6 down.Both B and C.
You Try #3 Describe the rotation from Figure A to Figure B. Give both CW and CCW description. Figure A Figure B
You Try #4 Which describes the rotation of the cell phone? Select ALL that apply. 90° clockwise 180º clockwise 270° clockwise90° counter-clockwise 180º counter-clockwise270° counter-clockwise
Moving on… Section 1: Describing RotationsSection 2: Graphing Rotations 180º
Graphing rotations Graphing a rotation can be very challenging. Most of us have difficulties envisioning what a figure will look like after a 90º , 180º or 270º turn. Rotate the figure below 180° clockwise about the origin.
Another Way Another method for graphing rotations is to apply some RULES.
Rotating 180º clockwise or counter-clockwise RULE: Keep the same coordinates; Change both signs to the opposite. (x, y) (-x, -y)EXAMPLE:Preimage ImageX(1, 2) X’(-1, -2)Y(3, 5) Y’(-3, -5)Z(-3,4) Z’(3, -4) Notice how image is upside down with a 180º rotation! https://www.youtube.com/watch?v=8ZeeDYIlNFk These means “take the opposite”, not “make it negative” !
Guided Practice Rotate ABC 180º clockwise about the origin
You Try Rotate Figure ABCD 180º clockwise about the origin
Guided Practice #1 Rotate EFG 180º clockwise about the origin. RULE:Keep the same coordinates;Change both signs to the opposite. (x, y) (-x, -y)
You Try #1 Rotate QRS 180º clockwise about the origin RULE: Keep the same coordinates;Change both signs to the opposite. (x, y) (-x, -y)
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More on… Graphing and Describing “Rotations” TransformationsDay 6
Prior… Yesterday, we began looking at “Rotations”. We focused on 180 . Today, we will learn how to graph 90° and 270° rotations.
Definition A rotation (turn) moves a figure around a point. This point can be on the figure or it can be some other point. This point is called the point of rotation . P
Moving on… Section 1: Graphing Rotations 90º Section 2: Graphing Rotations 270º
Another Way You can use RULES to graph 90° rotations that go about the origin .
Rotating 90ºclockwise RULE: Swap the x and y values; Change the sign of the 2 nd coordinate to the opposite. (x, y) (y, -x)EXAMPLE:Preimage ImageA(3, 5) A’(5, -3) B(4, 1) B’(1, -4)C(2, 1) C’(1, -2) https://www.youtube.com/watch?v=LwGmA9F3hbw Help on remembering which sign to change: A 90º clockwise rotation is a rotation going right . You change the sign on the right . These means “take the opposite”, not “make it negative” !
Rotating 90º Counter-Clockwise RULE: Swap the x and y values; Change the sign of the 1 st coordinate to its opposite. (x, y) (-y, x)EXAMPLE:Preimage ImageA(1, 2) A’(-2, 1)B(2, 3) B’(-3, 2)C(3, 1) C’(-1, 3) https://www.youtube.com/watch?v=4Q70ZHVFKPc Help on remembering which sign to change: A 90º counter -clockwise rotation is a rotation going left . You change the sign on the left . These means “take the opposite”, not “make it negative” !
Guided Practice #1 Rotate EFG 90º clockwise.
You Try #1 Rotate 90º clockwise .
Guided Practice #3 Rotate EFG 90º counter-clockwise.
You Try #3 Rotate 90º counter-clockwise .
Moving on… Section 1: Graphing Rotations 90º Section 2: Graphing Rotations 270º
270º Rotations If asked to rotate 270º clockwise… Follow the rule for 90º CCW . If asked to rotate 270º counter-clockwise… Follow the rule for 90º clockwise.
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