13.6 and 13.7

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# 13.6 and 13.7 - PowerPoint PPT Presentation

13.6 and 13.7. Rotations, Symmetry and Dilations. Goal Statement. w ill rotate figures and identify rotational symmetry w ill dilate figures in a coordinate plane. Can you identify the following terms?. r otation: center of rotation: angle of rotation:.

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### 13.6 and 13.7

Rotations, Symmetry and Dilations

Goal Statement
• will rotate figures and identify rotational symmetry
• will dilate figures in a coordinate plane
Can you identify the following terms?
• rotation:
• center of rotation:
• angle of rotation:
Can you identify the following terms?
• rotation: a transformation where a figure is turned about a fixed point
• center of rotation:
• angle of rotation:
Can you identify the following terms?
• rotation: a transformation where a figure is turned about a fixed point
• center of rotation: the fixed point (ex. 0,0)
• angle of rotation:
Can you identify the following terms?
• rotation: a transformation where a figure is turned about a fixed point
• center of rotation: the fixed point (ex. 0,0)
• angle of rotation: the number of degrees a figure moves clockwise or counterclockwise about the center of rotation
Angle of Rotation

-the number of degrees a figure moves clockwise or counterclockwiseabout the center of rotation

Angle of Rotation

-the number of degrees a figure moves clockwise or counterclockwiseabout the center of rotation

90º Clockwise Rotations

Do you see a way to find the image coordinates if you have the original coordinates?

90º Clockwise Rotations

Try:

Original Image

A (3, -5)

B (2, -4)

C (4, -1)

D (-1, 6)

Switch the coordinates and multiply the new y-coordinate by -1. (x,y) (y,-x)

90º Clockwise Rotations

Try:

Original Image

A (3, -5) A’ (-5, -3)

B (2, -4) B’ (-4, -2)

C (4, -1) C’ (-1, -4)

D (-1, 6) D’ (6, 1)

Switch the coordinates and multiply the new y-coordinate by -1. (x,y)  (y,-x)

90º Counterclockwise Rotations

Do you see a way to find the image coordinates if you have the original coordinates?

90º Counterclockwise Rotations

Try:

Original Image

A (3, -5)

B (2, -4)

C (4, -1)

D (-1, 6)

Switch the coordinates and multiply the new x-coordinate by -1. (x,y) (-y,x)

90º Counterclockwise Rotations

Try:

Original Image

A (3, -5) A’ (5,3)

B (2, 4) B’ (-4,2)

C (-4, 1) C’ (-1,-4)

D (-1, 6) D’ (-6,-1)

Switch the coordinates and multiply the new x-coordinate by -1. (x,y) (-y,x)

180º Rotations

To rotate a figure 180º about the origin, multiply each coordinate by -1. (x, y) → (-x, -y)

A family crest has rotational symmetry for

90º and 180º clockwise (or counterclockwise)

rotation.

Rotational Symmetry

A family crest has rotational symmetry for

90º and 180º clockwise (or counterclockwise)

rotation.

Rotational Symmetry

A family crest has rotational symmetry for

90º and 180º clockwise (or counterclockwise)

rotation.

Rotational Symmetry

A family crest has rotational symmetry for

90º and 180º clockwise (or counterclockwise)

rotation.

Rotational Symmetry
Dilations

-a transformation where a figure stretches or shrinks with respect to a fixed point (center of dilation – ex. 0,0)

-in a dilation, a figure and its image are similar

You can multiply the coordinates by a scale factor of 2.

You can multiply the coordinates by a scale factor of 2.

ie. (x,y) (2x,2y)

Or the thing you are multiplying by.

If your scale factor is 2, you multiply each coordinate by 2. If it is 0.5, you multiply by 0.5

OYO

Draw quadrilateral ABCD with vertices A(-1, 2), B(1, 2), C(3, 0), and D(-1, -1). Then find the coordinates of the vertices of the image after a dilation having a scale factor of 2, and draw the image.

OYO Solution

Draw quadrilateral ABCD with vertices A(-1, 2), B(1, 2), C(3, 0), and D(-1, -1). Then find the coordinates of the vertices of the image after a dilation having a scale factor of 2, and draw the image.

SOLUTION

A’ (-2, 4)

B’ (2, 4)

C’ (6, 0)

D’ (-2, -2)

OYO Solution (cont.)

Draw quadrilateral ABCD with vertices A(-1, 2), B(1, 2), C(3, 0), and D(-1, -1). Then find the coordinates of the vertices of the image after a dilation having a scale factor of 2, and draw the image.

SOLUTION

A’ (-2, 4)

B’ (2, 4)

C’ (6, 0)

D’ (-2, -2)

Finding a Scale Factor

To find a scale factor, divide the larger photo coordinates by the smaller photo coordinates (since it was an enlargement).

5/2 = 2.5 2.5/1 = 2.5

12.5/5 = 2.5 2.5/1 = 2.5

The scale factor is 2.5

Try:

Find the scale factor.

Solution: A’ to A is 3 / 0.5 = 6 and B’ to B is 6/1 = 6.

The scale factor is 6. The image (the enlarged line) is 6 times larger than the original line.

Homework

Green Challenge:

p.744 – 745 # 3 – 5 all, 8 – 13all, 15, 17 *3 graphs needed*

p.749 – 750 # 1, 5 – 10 all *4 graphs needed*

Blue Challenge:

p.744 – 746 # 9 – 19 (odd), 20 – 22 all *5 graphs needed*

p.749 – 751 # 1, 5 – 13all, 17, 18 *8 graphs needed*