Geometry Never, never, never give up. Winston Churchill Today: 9.4 Instruction Practice

GeometryNever, never, never give up.

Winston Churchill

Today: 9.4

Instruction Practice

Assignment:9.6 p 678 #19, 23,

26, 27, 28, 41, 42Homework Quiz

Chapter 7 on Thursday

Test Chapter 7 on Friday

Geometry

Never, never, never give up.

Winston Churchill

Objectives:1. Make composition transformations2. Identify types of composition

transformations

Vocabulary: glide reflection, composition

9.4 Glide Reflections and Compositions

composition – when two or more transformations are combined

glide reflection – a transformation of translation and a reflection

7.5

Vocabulary Review

Describe the composition.

7.5

Use the information below to sketch the image CD after a composition.

C(2, 0) and D(3, 3)

reflection: in the x-axis

rotation: 90° ccw

about the origin

7.5Is the composition a glide reflection?

Use the information below to sketch the image CD after a composition.

C(2, 0) and D(3, 3)

rotation: 90° ccw about the origin

reflection: in the x-axis

7.5Is the composition a glide reflection?

Will the composition be the same?

Use the information below to sketch the image QRS after a composition.

Q(2, -3), R(4, -4) and S(5, -1)

translation: (x, y) (x, y + 5)

reflection: about the y-axis

7.5Is the composition a glide reflection?

Use the information below to sketch the image EF after a composition.

E(-3, 5) and F(2, 7)

rotation: 180° cw about the origin

translation: (x, y) (x – 3, y + 1)

7.5Is the composition a glide reflection?

A

B C

A’

B’C’

Describe the composition.

A’’

B’’

C’’

7.5

1. Rotate 180° clockwise about (1, 1)

2. Translate (x, y) (x – 2, y + 4).

Describe the composition.

7.5

y

1. Reflect about the y-axis

2. Translate (x, y) (x, y + 2).

x0

A. (–3, –1)

B. (–6, –1)

C. (1, 6)

D. (–1, –6)

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''?

What transformations are needed to solve the puzzle?

7.5

What transformations are needed to solve the puzzle?

7.5

What transformations are needed to solve the puzzle?

7.5

What transformations are needed to solve the puzzle?

7.5

What transformations are needed to solve the puzzle?

7.5

Describe Transformations

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

Describe Transformations

Step 1 A brick is copied and translated to the right one brick length.

Describe Transformations

Step 2 The brick is then rotated 90°counterclockwise about point M, given here.

Describe Transformations

Step 3 The new brick is in place.

Answer: The pattern is created by successive translations and rotations shown above.

Describe Transformations

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

Describe Transformations

Step 1 Two bricks are copied and translated 1 brick length to the right.

Describe Transformations

Step 2 The two bricks are then rotated 90 clockwise or counterclockwise about point M, given here.

Describe Transformations

Step 3 The new bricks are in place.

Another transformation is possible.

Describe Transformations

Step 1 Two bricks are copied and rotated 90 clockwise about point M.

Describe Transformations

Step 2 The new bricks are in place.

Answer: The pattern is created by successive rotations of two bricks or by alternating translations then rotations.

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.

A. 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.

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

Assignment:9.4 p 656 #27, 29,

35, 41, 43, 45, 46Homework Quiz

Chapter 7 on Thursday

Test Chapter 7 on Friday

Geometry

Never, never, never give up.

Winston Churchill