Chapter 9 3 and 9 4
This presentation is the property of its rightful owner.
Sponsored Links
1 / 26

Chapter 9.3 and 9.4 PowerPoint PPT Presentation


  • 89 Views
  • Uploaded on
  • Presentation posted in: General

Chapter 9.3 and 9.4. Rotations and Compositions of Transformations. Rotations. A rotation is a turn that moves every point of an image through a specified angle and direction about a fixed point. Concept. Rotate 90°. Graph the point A (-2, 4)

Download Presentation

Chapter 9.3 and 9.4

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript


Chapter 9 3 and 9 4

Chapter 9.3 and 9.4

Rotations and Compositions of Transformations


Rotations

Rotations

  • A rotation is a turn that moves every point of an image through a specified angle and direction about a fixed point.


Concept

Concept


Rotate 90

Rotate 90°

  • Graph the point A

    (-2, 4)

  • Graph the image of A’ under a rotation of 90° counterclockwise about the origin


Rotate 180

Rotate 180°

  • Graph the point B

    (2, -5)

  • Graph the image of B’ under a rotation of 180° counterclockwise about the origin


Rotate 270

Rotate 270°

  • Graph the point C

    (-4, -6)

  • Graph the image of C’ under a rotation of 270° counterclockwise about the origin


Example 3

Example 3

Rotations in the Coordinate Plane

Hexagon DGJTSR is shown below. What is the image of point T after a 90 counterclockwise rotation about the origin?

A (5, –3)

B (–5, –3)

C (–3, 5)

D (3, –5)


Example 31

Example 3

Triangle PQR is shown below. What is the image of point Q after a 90° counterclockwise rotation about the origin?

A.(–5, –4)

B.(–5, 4)

C.(5, 4)

D.(4, –5)


Chapter 9 3 and 9 4

Rotations in the Coordinate Plane

Triangle DEF has vertices D(–2, –1), E(–1, 1), and F(1, –1). Graph ΔDEF and its image after a rotation of 90° counterclockwise about the origin.


Chapter 9 3 and 9 4

Rotations in the Coordinate Plane

Line segment XY has vertices X(0, 4) and Y(5, 1). Graph XY and its image after a rotation of 270° counterclockwise about the origin.


Composition of transformations

Composition of transformations

  • When a transformation is applied to a figure and then another transformation is applied to its image, the result is called a composition of transformations.


Concept1

Concept


Example 1

Example 1

Graph a Glide Reflection

Quadrilateral BGTS has vertices B(–3, 4), G(–1, 3), T(–1 , 1), and S(–4, 2). Graph BGTS and its image after a translation along 5, 0 and a reflection in the x-axis.


Example 11

Example 1

Quadrilateral RSTU has vertices R(1, –1), S(4, –2), T(3, –4), and U(1, –3). Graph RSTU and its image after a translation along –4, 1and a reflection in the x-axis. Which point is located at (–3, 0)?

A.R'

B.S'

C.T'

D.U'


Example 2

Example 2

Graph Other Compositions of Isometries

ΔTUV has vertices T(2, –1), U(5, –2), and V(3, –4). Graph ΔTUV and its image after a translation along –1 , 5 and a rotation 180° about the origin.


Example 21

Example 2

ΔJKL has vertices J(2, 3), K(5, 2), and L(3, 0). Graph ΔTUV and its image after a translation along 3, 1and a rotation 180° about the origin. What are the new coordinates of L''?

A.(–3, –1)

B.(–6, –1)

C.(1, 6)

D.(–1, –6)


Concept2

Concept


Concept3

Concept


Example 32

Example 3

Reflect a Figure in Two Lines

Copy and reflect figure EFGH in line p and then line q. Then describe a single transformation that maps EFGH onto E''F''G''H''.


Example 33

Example 3

Reflect a Figure in Two Lines

Step 1Reflect EFGH in line p.


Example 34

Example 3

Reflect a Figure in Two Lines

Step 2Reflect E'F'G'H' in line q.

Answer:EFGH is transformed onto E''F''G''H'' by a translation down a distance that is twice the distance between lines p and q.


Example 35

Example 3

Copy and reflect figure ABC in line s and then line t. Then describe a single transformation that maps ABC onto A''B''C''.

A.ABC is reflected across lines and translated down 2 inches.

B.ABC is translated down 2 inches onto A''B''C''.

C.ABC is translated down 2 inches and reflected across line t.

D.ABC is translated down 4 inches onto A''B''C''.


Example 4

Example 4

Describe Transformations

A. LANDSCAPING Describe the transformations that are combined to create the brick pattern shown.


Example 41

Example 4

Describe Transformations

B. LANDSCAPING Describe the transformations that are combined to create the brick pattern shown.


Example 42

Example 4

A. What transformation must occur to the brick at point M to further complete the pattern shown here?

A.The brick must be rotated 180° counterclockwise about point M.

B.The brick must be translated one brick width right of point M.

C.The brick must be rotated 90° counterclockwise about point M.

D.The brick must be rotated 360° counterclockwise about point M.


Example 43

Example 4

B. What transformation must occur to the brick at point M to further complete the pattern shown here?

A.The two bricks must be translated one brick length to the right of point M.

B.The two bricks must be translated one brick length down from point M.

C.The two bricks must be rotated 180° counterclockwise about point M.

D.The two bricks must be rotated 90° counterclockwise about point M.


  • Login