unit 1 topic 2 - math with mrs. pierce...match each verbal translation with its algebraic...

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Unit 1 Topic 2 Transformations

Name: ________________________________

Teacher: _____________________

Period: _______________

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SLT 7 – Transformation Classification

Rotation Reflection

Translation Other

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Classify each Transformation

A

B

C

D

E

F

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Classify each Transformation

G

H

I J

L

K

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1. Why are reflections, rotations, and transformations referred to as “rigid” transformations?

a. They all involve movement.

b. They all reserve the size of the shape/figure.

c. They all make the shape larger.

d. They all can only move in certain ways.

2. Sketch the resulting figure after it is reflected over the line:

3. Draw the shape below after a 90, 180, 270, and 360 degree rotation clockwise

Pre-image: 90 degree rotation

180 degree rotation

270 degree rotation

360 degree rotation

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4. Using the figure below create, provide an example of a reflection, rotation, and translation

Preimage:

Reflection:

Translation:

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Rotation 90 degrees counterclockwise around

point M:

M

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SLT 8 – Room Layout

You are finally getting your own room. The room layout you created is based on the dimensions of the room

(14 feet x 14 feet) and the dimensions of the furniture. Below is the design you came up with (each unit square

represents one square foot):

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Name: _________________

SLT 8 – Coordinate Furniture

Your parents look at the layout you designed and ask you to make a few changes:

• Move the desk/chair combo one unit to the right for space to plug in electronics.

• Move the TV three units up because of the placement of a window.

• Move the bed up one unit and one unit to the right so that it touches both walls.

• Move the couch two units to the left because of the placement of a closet.

• Move the coffee table one unit to the left to be centered in front of the couch.

• Move the rug two units to the right and one unit up.

• The nightstand can stay in its current location.

• Move the book shelf one unit down because of the placement of the door.

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Desk Top left point Rule:

Old

New

Night Stand

Top left point Rule:

Old

New

Coffee Table


Old

New

Book Shelf


Old

New

Chair Top left point Rule:

Old

New

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Rug Top left point Rule:

Old

New

TV Top left point Rule:

Old

New

Couch Top left point Rule:

Old

New

Bed Top left point Rule:

Old

New

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SLT 9 – Describe & Draw Horizontal and Vertical Translations; Describe using Function Notation

Describing Translations

Description:

Coordinate notation:

Description:


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Description:


Description:


Description:


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Description:


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7) The vertices of triangle DEF are , and . The translation of triangle DEF to

triangle is described by the notation .

Graph triangle DEF (pre-image) and triangle (image) and identify the coordinates of triangle

.

8) The vertices of the figure (image) are , , , and . The translation

of figure ABCD (pre-image) to figure (image) is described by the notation .

Graph figure ABCD (pre-image) and (image) and identify the coordinates of figure ABCD.

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9) The vertices of triangle KLM are , ), and . A translation of triangle KLM (pre-image)

results in triangle (image) with vertices , , and . Graph the figure and

use words and coordinate notation to describe the translation.

10) The vertices of figure RSTU are , , , and . A translation of figure RSTU

(pre-image) results in figure (image) with vertices , , , and .

Graph the figure and use words and coordinate notation to describe the translation.

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11) Use coordinate notation to describe the translations:

3 units to the left, 1 unit down

8 units to the right, 2 units up

6 units to the right, 4 units down

7 units to the left, 9 units up

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SLT 8-9

Describe and draw vertical and horizontal translations and write the associated function with inputs and outputs.

1. For each question below, perform the indicated translation and draw the resulting figure. Be sure to label your image.

List the coordinates (x,y) for both the pre-image and image:

A: _____________ A’: _____________

B: _____________ B’: _____________

C: _____________ C’: _____________

D: _____________ D’: _____________

How did each x value change?

How did each y value change?

Let’s write a rule for this translation:

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2. For each question below, perform the indicated translation and draw the resulting figure. Be sure to label your image.

List the coordinates (x,y) for both the pre-image and image:

D: _____________ D’: _____________

E: _____________ E’: _____________

F: _____________ F’: _____________

How did each x value change?

How did each y value change?

Let’s write a rule for this translation:

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3. Match each verbal translation with its algebraic equivalent.

Left two units and up five units

(x + 4, y – 3)

Right four units and down three units

(x + 7, y – 3)

Up four units and down four units.

(x – 7, y + 4)

Up four units and left seven units

(x – 2, y + 5)

Down two units and right eight units

(x + 8, y – 2)

Right seven units and down three units

(x + 2, y)

Left two units and right four units.

(x , y)

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4. For each graph shown below, write the transformation and the rule used to translate the pre-image to the image. Also,

identify the coordinates of the preimage and image:

R: _____________ R’: _____________ A: _____________ A’: _____________

S: _____________ S’: _____________ B: _____________ B’: _____________

Q: _____________ Q’: _____________ C: _____________ C’: _____________

T: _____________ T’: _____________

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SLT 10

Describe and draw reflections.

1. Quadrilateral QRST is going to be reflected about line “m”. Draw the reflection of QRST and be sure to

label the new figure Q’R’S’T’ with the vertices correctly placed.

2. Triangle DEF will be reflected twice, first over line “p” and then a second time over line “n”. Correctly

draw and label the two new images.

Q S

D

E F

m

n

R

T

p

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SLT 10 & 11 – Describe & Draw Reflections

Reflect This

1) Reflect the triangle and rectangle across the x-axis and record the image on the coordinate plane.

2) Reflect the triangle and rectangle across the y-axis and record the image on the coordinate plane.

3) Reflect the triangle and rectangle across the line y = x and record the image on the coordinate plane

Reflections Practice

Given the pre-image, sketch the image across the line of reflection, label the image’s vertices and complete the

missing parts of each of the statements.

A

B C

D

E F

G

E

F

G

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1) 2) 𝐴𝐵𝐶𝐷 → ________________ ∆𝐸𝐹𝐺 → ________________

𝐶𝐷̅̅ ̅̅ ≅ _______________ 𝐸𝐹̅̅ ̅̅ ≅ _______________

𝐵𝐶̅̅ ̅̅ ≅ _______________ 𝐹𝐺̅̅ ̅̅ ≅ _______________

𝐴𝐵̅̅ ̅̅ ≅ _______________ 𝐸𝐺̅̅ ̅̅ ≅ _______________

𝐷𝐴̅̅ ̅̅ ≅ _______________

3)

𝐻𝐽𝐾𝐿 → ________________

𝐾𝐿̅̅ ̅̅ ≅ _______________

𝐻𝐽̅̅̅̅ ≅ _______________

𝐿𝐻̅̅ ̅̅ ≅ _______________

𝐽𝐾̅̅ ̅ ≅ _______________

4) In the figure below, there is a reflection that transforms 𝑊𝑋𝑌𝑍 to 𝑊′𝑋′𝑌′𝑍′.

Use a straightedge and compass to construct the line of reflection and list the steps of the construction.

A B

C D

H J

K L

X

𝑊′

𝑋′

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SLT 11

Draw a reflection when given a rule and write a rule given a reflection

1. Follow the written rule to perform each reflection below. Be sure to identify the coordinates of the pre-image as well as the image. Then,

write the algebraic rule that corresponds.

M M’

N N’

O O’

Q Q’

R R’

S S’

T T’

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M M’

N N’

L L’

H H’

I I’

J J’

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2. Point A lies in the coordinate grid at the location (2, -3). Write the resulting coordinates of point A if it is transformed in the manner described

below (use a graph if necessary):

a. Reflected over the x-axis __________________

b. Reflected over the y-axis __________________

c. Reflected over the line y = 4 _________________

d. Reflected over the line x = 2 ________________

e. Reflected over the x-axis and then the y-axis _______________

f. Reflected over the line y = x ___________________

g. *Reflected over the x-axis and

then moved down four units _______________

h. * Moved down four units and

then reflected over the x-axis _______________

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3. Triangle ABC is shown below. Draw the line y = 1 on the graph. Reflect triangle ABC across the line

y = 1. Be sure to label the resulting points.

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SLT 13 – Describe & Draw Rotations

Exploring Rotations

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Clockwise Rotation:

Starting Coordinates 90 degrees 180 degrees 270 degrees 360 degrees

RULE:

Counter-Clockwise Rotation:

Starting Coordinates 90 degrees 180 degrees 270 degrees 360 degrees

RULE:


Rotations Practice

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SLT 17 – Combine Transformations and Write the Associated Function

A Series of Transformations

1) Reflect triangle across the x-axis. Translate the image 7 units to the right.

Pre-image Image Final Image

B

C

Rule:

2) Translate triangle 7 units to the right. Reflect the image across the x-axis.


A

B

C

Rule:

What do you notice about the two triangles that result from the series of transformations?

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3) Rotate triangle counterclockwise. Translate the image 8 units down.


D

E

F

Rule:

4) Translate triangle figure 8 units down. Rotate the image counterclockwise.


D

E

F

Rule:

What do you notice about the two triangles that result from the series of transformations?

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5) Reflect figure across the y-axis. Reflect the image across the x-axis.


A

B

C

D

Rule:

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6) Reflect figure across the line . Reflect the image across the y-axis.


A

B

C

D

E

Rule:

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SLT 16 – Combine Transformations and Write the Associated Functions

2. Phillip told his teacher that some multi-step transformations could be accomplished using just one step.

The teacher then asked the other students what they thought. Do you agree or disagree with Phillip? If

you agree, provide at least one example. You can use sketches, words, and/or numbers in your

explanation.

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4. Jared takes the pre-image of a triangle and reflects it over the y-axis and then translates it left two units.

Jenny did the same problem but translated the triangle left two units and then reflected it over the y-axis.

Did Jenny and Jared end up with the same image? Explain.

5. Write a verbal representation of each transformation below:

a. F(x, y) = (-x, y + 7)___________________________________________

b. F(x, y) = (x – 3, y + 2) ___________________________________________

c. F(x, y) = (x + 2, -y) ___________________________________________

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SLT 12-13

Describe and draw rotations of 90 degrees clockwise and counter clockwise. Draw a rotation when given a rule with inputs and outputs and write a rule for a given rotation.

1. Which of the following criteria are necessary to successfully describe a rotation in the coordinate plane?

Place a check next to the ones that are necessary and an x next to the ones that are not.

______Center of rotation

______Axis of Symmetry

______Angle of Rotation

______Size of the object

______Direction of rotation

2. In the figure below, state the angle of rotation and state the direction.

3. Rotate the figure below 90 degrees

clockwise about the origin.

4. Rotate the figure below 90 degrees

counter-clockwise about the origin

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5. Derrick says that a rotation 90 degree clockwise is the same as rotation 270 degrees counter-clockwise.

Do you agree or disagree? Why?

D D’

E E’

F F’

A A’

B B’

C C’

unit 1 topic 2 - math with mrs. pierce...match each verbal translation with its algebraic...

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