Unit 1 Modeling with Geometry: Transformations€¦ · Common Core Math 2 Unit 1A Modeling with...

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Name:____________________________ Period: _____

Unit 1

Modeling with Geometry:

Transformations

Common Core Math 2 Unit 1A Modeling with Geometry: Transformations

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Unit Skills I can: Use prime notation to distinguish an image from its pre-image. (G-CO.2) Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel

lines, and line segments. (G-CO.4) Verify experimentally the properties of transformations. (8-G.1, G-SRT.1) Compare transformations that preserve distance and angle (rigid motions) to those that do not (e.g. dilation or

horizontal stretch). (G-CO.2) I can describe transformations. Determine whether a single transformation is a translation, reflection, rotation, or dilation. Given a pre-image and its translated image, I can determine the translation vector. Given a pre-image and its reflected image, I can determine the line of reflection. Given a pre-image and its rotated image, I can determine the center and angle of rotation. Given a pre-image and its dilated image, I can determine the scale factor. Given a pre-image and its translated image graphed on the coordinate plane, I can give a function rule for the

horizontal and vertical change and describe the translation verbally. Given a pre-image and its reflected image graphed on the coordinate plane, I can determine the line of reflection,

give a function rule for the reflection, and describe the reflection verbally. Given a pre-image and its rotated image of 90 clockwise, 90 counterclockwise, or 180 in the coordinate plane, I

can give a function rule for the rotation and describe the rotation verbally. Given a pre-image and its dilated image on the coordinate plane with center at (0, 0), I can give a function rule for

the dilation and describe the dilation verbally. I can draw transformations. Given a translation vector, I can draw the translation of a figure on plain paper. Draw the translation of a figure on the coordinate plane given a verbal or algebraic description of the horizontal and

vertical change. Given the line of reflection, I can draw the reflection of a figure on plain paper. Given a horizontal or vertical line of reflection or function rule, I can draw the reflection of a figure on the coordinate

plane. Given the center of rotation and angle of rotation, I can draw the rotation of a figure on plain paper. Given a verbal description or function rule, I can draw a rotation of 90 clockwise, 90 counterclockwise, or 180 of

a figure on the coordinate plane. Given a scale factor and center of dilation, I can draw the dilation of a figure on plain paper. Given a scale factor or function rule, I can draw a dilation of a figure on the coordinate plane with center of dilation

at (0, 0). Use dynamic geometry software to perform transformations. I can apply transformations. Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it

onto itself. Perform multiple transformations on a given figure. Specify a sequence of transformations that will carry a given figure onto another. Applications: Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle. Find the point on a directed line segment between two given points that partitions the segment in a given ratio. Modeling: Identify the shape of a cross-section of a three dimensional object. Identify the three dimensional figure generated by the rotation of a two-dimensional shape. Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a

human torso as a cylinder). Apply concepts of density based on area and volume in modeling situations (e.g., persons per square mile, BTUs per

cubic foot). Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical

constraints or minimize cost; working with typographic grid systems based on ratios).


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Vocabulary: Define each word and give examples and notes that will help you remember the word/phrase.

Angle of Rotation

Example and Notes to help YOU remember:

Center of Rotation


Congruent


Image


Line of Reflection


Prime Notation



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Reflection


Rigid Motion


Rotation


Transformation


Translation


Vector



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Part 1: Introduction to Transformations

Geometrical Transformation – a change in the _______________, _______________ or _______________ of a

geometrical figure. Types of Transformations

Rigid motion (___________________________)

preserves the _______________ and _______________

__________________

__________________

__________________

Non-rigid

__________________

Transformations are functions that take points in the plane as _______________ and give other points as _______________.

Pre-image: _______________________

Image: _______________________

Prime Notation: to distinguish the pre-image from the image

Input points ____________ Output points _____________

Example 1: Is this rigid motion? Example 2: Is this rigid motion? (different scale from #1) (x,y) (x-4,y+2) (x,y) (2x,2y) pre-image image pre-image image A(0,0) A(0,0)

B(2,0) B(2,0)

C(0,4) C(0,4)


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Part 2: Translations Translation is a transformation that _________________ all points of an image a _________________ distance is a

given ______________.

Lines that _________________ corresponding points of a pre-image and

its translated image are _________________.

_________________ segments of the pre-image and its translated image

are also _________________.

Types of notations for translations

Descriptive Notation: __________________________________________________________________

Example

Coordinate Notation (function rule): _____________________________________________________

__________________________________________________________________________________

Example: T(x,y) (x+2, y-3)

Vector Notation

o A vector has ______________ and _______________

o denoted by <a,b> “a” specifies a ___________________ change

“b” specifies a ___________________ change

negative: move _______________ or ______________

T<2,-3>(x+2, y-3)

A

B

C


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Transformation HW (©2011 Kuta Software LLC. All rights reserved.)


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Marching Band Translation: You are designing the half-time show for the home-coming game. Each band member will move from their original location to a new location based on the rule you give each student. Be creative with your final scene because you really want to impress the audience! (This is your worksheet) On the Top portion: Graph and label each original location. Move each member to a new location. Graph and label the new point. Write the rule for the translation. On the bottom portion: Write the rules on the bottom table. Cut off the bottom part and give to your partner who will try to recreate your pattern. Write Lift Next to the RULE of the stop point if you need your partner to start a new line.

Pre-Image Image Rule

A(-7,4)

B(-7, 0)

C(-4,0) Lift

D(-2, 0)

E(-2,4)

F(0,0)

H(2,4)

I(2,0) Lift

J (4,0)

K(7,0)

L(7,2)

M(4,2)

N(4,4)

O(7,4)

Pre-Image Image Rule

A(-7,4)

B(-7, 0)

C(-4,0) Lift

D(-2, 0)

E(-2,4)

F(0,0)

H(2,4)

I(2,0) Lift

J (4,0)

K(7,0)

L(7,2)

M(4,2)

N(4,4)

O(7,4)

Designer’s Name ____________________ #_____ Partner’s Name _____________________ # ____

Partner: DO NOT DRAW THE PRE-IMAGES. Graph the image point you found and connect the dots to make picture


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Page Left Blank Intentionally


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Part 3: Reflections

A ________________ is a transformation that ______________ all points of an image over a line called the

________________ _______ ______________________ (LOR).

The LOR is the __________________ ______________ of each segment joining each

point and its _____________.

Points are ______________________ from the LOR.

Reflection Notation:

rk (ABC) =

Glue paper here


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Drawing a Reflection: 1: Through each ___________ draw a line perpendicular to the LOR.

2: Measure the distance from each vertex to the LOR. Locate

the __________ of each vertex on the ______________ side

of the LOR and the ___________ distance from it.

3: Connect the vertices

Reflection over x-axis Reflection over y-axis

rx-axis= (x,y) ry-axis= (x,y)

Reflection over y = x or y = -x Reflection over any line

ry=x= (x,y) A reflection can occur across any line

ry=-x= (x,y)


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Reflections HW (©2011 Kuta Software LLC. All rights reserved.)


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Part 4: Rotations

A ________________ is a transformation that _______________ all points of a figure around a _____________ point

called the ___________________ _______ _____________________ (COR).

The ______________ of rotation is the number of _______________ thorough

which points rotate around the COR.

Positive ________________________ Negative ________________________

A rotation is a transformation about a point P such that

• every point and its image are the ____________ _________________ from P (lie on a ________________)

• all _______________ with vertex P formed by a point and its image have the same ________________ Notation

RP, θ (ABC) = A’B’C’

Rotation of 90°: R90°(x,y) _________

Rotation of 180°: R90°(x,y) _________

Rotation of 270°: R90°(x,y) _________


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Rotation HW (©2011 Kuta Software LLC. All rights reserved.)


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Rotations with calculator

Figure being used will be a triangle: A(1,1), B(6,3), C(4,7).

1. Clear entries in the Y= positions (or turn them off).

2. Turn on the Connected Graph icon under StatPlots. Go to StatPlot - #1 Plot - highlight On - highlight second icon. Xlist is the name of the list where the x-coordinates will be found. Ylist is the name of the list where the y-coordinates will be found. Mark: choose the heavier mark to represent the original figure.

3. Enter values into L1 and L2. Enter the x-coordinate in L1 and its corresponding y-coordinate in L2. Enter the first coordinate again at the end to complete the connected drawing. The original triangle is now residing in Plot1. When graphing do NOT choose ZoomStat for the window. We want to have a coordinate axes for examining our transformations. Use a standard 10x10 window (ZStandard) for this problem.

4. We will be placing our transformation coordinates into L3 and our transformation figure will reside in Plot2.

Rotation of 90° counterclockwise: (x, y) → (-y, x)

Store the negated y-values into list L3. You can type them in yourself or let the calculator create the values. Arrow up ONTO L3 and enter -L2 (to negate the y-values). Press ENTER.

Rotation of 180° counterclockwise: (x, y) → (-x, -y)

Store the negated x-values into list L3 and the negated y-values in L4. Under Plot 2, assign Xlist: L3 and Ylist: Y4. Graph.

Rotation of 270° counterclockwise: Try this on your own.


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Create your own figure

1. Draw a figure in quadrant 1 with at least 5 sides 2. In the table, write the transformed coordinates for each rotation. Use a different color for each rotation. Plot

the transformed shapes in the matching color on the coordinate plane.

Point 90° 180° 270°

Answer the following questions:

For the 90° rotation, why did you plot L3 as the x-list and L1 as the y-list? For the 180° rotation, you had to create list Y4. Why did you create this list? Explain how you created the 270° rotation.


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Part 4: Dilation Dilation is a transformation that produces an image ________________ to the original by ______________________

shrinking or stretching the _____________ of the pre-image. Similar images have __________ shape and _______________ size. Scale Factor (k): _____________ of the lengths of the _________________ dimensions in similar images.

(ie., sides or area) Notation:

Dk , O(x, y) = (kx, ky)

k =A′B′

AB , O is the center of dilation

If O is a fixed point and A’ is the image of A, then 0, A and A’ are _____________ and k = ________.

Enlarge: k___________ Reduce: _______________ k ______________ Center of Dilation is the _________ point about which all points are ______________ or ___________________.

Given rectangle ABCD, find the dilation with a scale of 2/3.

A(-6,-3)

B(-6,3)

C(6,3)

D(6,-3)


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Determine the scale factor

Dilation from an arbitrary point Dilate the following k = 3 from point (10, -10)

A(7,-8)

B(5,-8)

C(5,-3)

D(9,-3)

E(9,-5)

F(7,-5)

x distance from P to A: _____

x distance from P to A’: _____

x value of A’: _____

y distance from P to A: _____

y distance from P to A’: _____

y value of A’: _____


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Dilations HW (©2013 Kuta Software LLC. All rights reserved.)


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2nd

Bedroom

1st

2.5 cm

2.5 cm 2.3 cm

2.3 cm

2.5

cm

2

.6 c

m

1.6

cm

0.4 cm

1.2 cm 1.3 cm

2.2

cm

2

.8 c

m

Floor Plan Comparison Use these two-bedroom apartment floor plans to complete the tables and answer the questions below on your own paper.

The scale factor for Apartment 1 is: 1 cm = 5 ft Apartment 1:

Room Blueprint

Dimensions (cm)

Actual Dimensions

Area

Master Bedroom

2nd Bedroom

Living Room 2.1x2.1

Kitchen 1.5x 1.7

Bathroom

Entry Way 1.2 x 1.7

Closet w/2nd BR

0.8x 0.5

The scale factor for Apartment 2 is: 1 cm = 4 ft Apartment 2:

Room Blueprint

Dimensions (cm)

Actual Dimensions

Area

1st Bedroom

2.5x 2.6

2nd Bedroom

Living Room

Kitchen

Bathroom 1.3x 1.6

Hall & Hall Closets

1.2x 2.0

Closet w/1st BR

1.3x 0.4

1. Calculate the total square footage of Apartment 1 and Apartment 2.

2. Apartment 1 rents for $550 per month. What is the price per square foot for Apartment 1?

3. Apartment 2 rents for $500 per month. What is the price per square foot for Apartment 2?

4. There are advantages and disadvantages to both apartments. Considering the various factors represented here in

the plans and calculations, which apartment would you prefer to rent, and why? (There is not one correct choice

here, but you should support your choice with multiple reasons using complete sentences and proper grammar and

spelling.)

Apartment 1 Apartment 2


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HW: Dilations Day 2


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Composite Transformations When we perform two or more transformations on an image, it is called a COMPOSITE TRANSFORMATION. If we called the first transformation R and the second transformation P, then we have:

R(ABC) = A’B’C’ and P(A’B’C’) = A’’B’’C’’ We can put these together as a composition:

PoR = P(R(ABC)) = A’’B’’C’’ Example 1 Translate down 3, right 2 then reflect over the x-axis

1. Write a rule for the first transformation

(x, y) (__________, ___________ )

2. Use the results from the first translation and write a rule for the 2nd transformation

(__________, ___________ ) (__________, ___________ )

Example 2 1. Using a ruler, measure from each point to line l to create the reflection A’B’C’. Label the points.

2. Next, measure from each point to line m to create the reflection A’’B’’C’’. Label the points.

3. Create a line from A to A’ to A’’. Measure the of AA’ and AA’’. mAA’ = __________ mAA”” = __________

Answer the following questions. What do you notice about AA’ and AA’’? How else could you write this transformation?

A

B

C

l m


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This is called the Parallel Lines Theorem of Reflection

Example 3: 1. Reflect the polygon across line l and then across line m.

2. Draw a line from point X to D and D””. 3. With a protractor, measure the angle create by DX and D’’X.

DXD”” = _______

4. Measure RXS.

RXS = _______

Answer the following questions.

What do you notice about DXD’’ and RXS? How else could you write this transformation? This is called the Intersecting Lines Theorem of Reflection

m

R

l

R X

X


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HW Composition of Transformations Part 1 All rectangles in the grid below are congruent. Follow the instructions and then write the number of the rectangle that matches the location of the final image. Rectangles may be used more than once. Which rectangle is the final image of each transformation?

1. Reflect Rectangle 1 over the y-axis. Then translate down three units and rotate 90° counterclockwise

around the point (3, 1). (Hint: redraw the axes so that the origin corresponds to (3, 1).)

2. Translate Rectangle 2 down one unit and reflect over the x-axis. Then reflect over the line x = 4.

3. Reflect Rectangle 3 over the y-axis and then rotate 90° clockwise around the point (-2, 0). Finally, glide

five units to the right.

4. Rotate Rectangle 4 90° clockwise around the point (-3, 0). Reflect over the line y = 2 and then translate

one unit left.

5. Translate Rectangle 5 left five units. Rotate 90° clockwise around the point (-2, 2) and glide up two

spaces.

6. Rotate Rectangle 6 90° clockwise around the point (4, 4) and translate down three units.

7. Rotate Rectangle 7 90° clockwise around (-4, 4) and reflect over the line x = -4.

8. Reflect Rectangle 8 over the x-axis. Translate four units left and reflect over the line y = 1.5.

1

8

5

4 3

2 7

6


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Composition of Motion Algebraic Rules Part 2 For each problem, there is a composition of motions. Using your algebraic rules, come up with a new rule after both transformations have taken place. If needed, you may use the coordinate plane below to help you determine the rule. 1) Translate a triangle 4 units right and 2 units up, and then reflect the triangle over the line y = x. 2) Rotate a triangle 90 degrees counter clockwise, and then dilate the figure by a scale factor of 3. 3) Translate a triangle 4 units left and 2 units down, and then reflect the triangle over the y-axis. 4) Rotate a triangle 90 degrees clockwise, and then dilate the figure by a scale factor of 1/3. 5) Translate a triangle 4 units right and 2 units down, and then reflect the triangle over the x-axis. 6) Rotate a triangle 180 degrees counter clockwise, and then dilate the figure by a scale factor of 2. 7) Translate a triangle 4 units left and 2 units up, and then reflect the triangle over the line y = x. 8) Rotate a triangle 180 degrees clockwise, and then dilate the figure by a scale factor of 1/2.


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Interpreting Functions

Warm-Up: Kim and Jim are twins and live at

the same home. They each walk to

school along the same path at

exactly the same speed. However,

Jim likes to arrive at school early

and Kim is happy to arrive 7

minutes later, just as the bell

rings. Pictured at right is a graph

of Jim’s distance from school over

time.

1. Use a dotted line to

sketch Kim’s graph of

distance from school

over time

(once she leaves for school).

2. How many minutes after 7AM does Jim leave for school? _____________

3. How many minutes after 7AM does Jim arrive at school? _____________

4. How many minutes after 7AM does Kim leave for school? _____________

5. How many minutes after 7AM does Kim arrive at school? _____________

6. What is Jim’s farthest distance from school? _____________

7. What is Jim’s closest distance to school? _____________

8. What is Kim’s farthest distance from school? _____________

9. What is Kim’s closest distance to school? _____________

Use your answers to the above questions to fill in the following:

Jim’s domain: _______ ≤ x ≤ _________ (where x represents time after 7AM)

Jim’s range: _______ ≤ y ≤ _________ (where y represents distance from school)

Kim’s domain: _______ ≤ x ≤ _________ (where x represents time after 7AM)

Kim’s range: _______ ≤ y ≤ _________ (where y represents distance from school)

Extend: Kim’s graph is a horizontal translation of Jim’s graph. When a graph translates horizontally,

how do the domain and range change?

Domain and Range in translations


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Quick review: The domain is the set of all possible x-values on the graph. The range is the set of all

possible y-values on the graph.

1. Describe the translation(s) from the pre-image to the image.

a. Given the following graph, state the domain and range of

the pre-image:

Domain: ____________Range: _____________.

b. State the domain and range of the image:

Domain: ____________Range: _____________.

2. Draw and label the image of AB translated left 2 and down 3.

a. State the domain and range of the pre-image:

Domain: ____________Range: _____________.


Domain: ____________Range: _____________.

3. Draw and label the image of AB reflected over the x-axis.


Domain: ____________Range: _____________.


Domain: ____________Range: _____________.

4. Draw and label the image of AB reflected over the y-axis


Domain: ____________Range: _____________.


Domain: ____________Range: _____________.


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5. Draw and label the image of AB reflected over the line y = x.


Domain: ____________Range: _____________.


Domain: ____________Range: _____________.

6. Draw and label the image of AB rotated 90°.


Domain: ____________Range: _____________.


Domain: ____________Range: _____________.

7. Draw and label the image of AB dilated by a factor of 3 with a center of (0,0)


Domain: ____________Range: _____________.


Domain: ____________Range: _____________.


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Homework Domain & Range

Given the patterns seen above, can you predict the domain/range of an image

given a pre-image domain/range? Let’s try:

1. Given a relation composed of points A(2,5), B(1, -6), and C(4, 7),

a. State the domain and range of the relation:

D: {_________} R: {_________}

b. State the domain and range of the image when the relation is:

i. Translated right 2 and down 3 :

D: {_________} R: {_________}

ii. Reflected in the x-axis:

D: {_________} R: {_________}

iii. Reflected in the y-axis:

D: {_________} R: {_________}

iv. Reflected in the line y=x:

D: {_________} R: {_________}

v. Rotated 90°:

D: {_________} R: {_________}

vi. Dilated by a factor of 7 with a center of (0, 0):

D: {_________} R: {_________}

2. Given a line segment with endpoints (0,4) inclusive and (3,0) exclusive

a. State the domain and range of the segment. D: _________ R: _________

b. State the domain and range of the image when the relation is:

i. Translated right 2 and down 3 :

D: ______________

R: ______________

ii. Reflected in the x-axis:

D: ______________

R: ______________

iii. Reflected in the y-axis:

D: ______________

R: ______________

iv. Reflected in the line y=x:

D: ______________

R: ______________

v. Rotated 90°:

D: ______________

R: ______________

vi. Dilated by a factor of 7 with a center of (0, 0):

D: ______________

R: _____________

Side note about notation: ** Discrete values must be represented by a list of values

written in this notation: { 1, 5, 7}

Interval notation: Represents the domain and range with a pair of numbers. [ ] for inclusive (≤ or ≥) and ( ) are used

for exclusive (< or >). Example: 3<x≤12 is equivalent to (3, 12]

Note: - and are always exclusive


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Basic Transformations and Algebraic Rules

Translations (Slide)

Function Rule (x, y)→

Vector Rule

Picture

Reflection (Flip)

Reflect over x-axis (x, y)→

Reflect over y-axis (x, y)→

Reflect over both axes (same as a 180° rotation)

(x, y)→

Reflect over y = x (x, y)→

Reflect over y = -x (x, y)→

Picture

Rotations

90° rotation (counter-clockwise)

(x, y)→

180° rotation (same as a reflection around both axes)

(x, y)→

270° rotation (counter-clockwise)

(x, y)→

360° rotation (x, y)→

Picture

Dilation (By a factor a, centered on the origin)

a>1, __________ (x, y)→

0<a<1, __________

Picture


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Unit 1A Review For each problem below Write the algebraic (arrow) rule for each transformation and the image points. Use graph paper if necessary. 1. MNO with M(-5,2), N(0, 4), and O(4, 5); translate left 6 and down 2. 2. Quadrilateral PQRS with P(-5, 1), Q(-2,6), R(3, 7), and S(6, 4); dilate d = 6 3. Pentagon PENTA with P(0, 2), E(4,6), N(8, -1), T(6, -3), and A(2, -4); reflect across y-axis. 4. RST with R(7,4), S(5,-3), and T(2, 6); reflected across the y = x axis. 5. FGH with F(-6,8), G(-3,-1), and H(0, 4); reflected across the x-axis, then reflected across the y-axis. 6. Rectangle ABCD with A(0,0), B(0,4), C(5,4), and D(5,0); rotate 90° clockwise. 7. XYZ with X(-2, 2), Y(4, 2), and Z(1, -5); rotate 180° clockwise. 8. Pentagon MNOPQ with M(-4, 1), N(-2, 3), O(0, 3), P(4, 3), and Q(2, -7); rotate 90° counterclockwise, then dilate by d = 4. 9. MNO with M(-5,2), N(0, 4), and O(4, 5); translate up 6.


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10. Quadrilateral PQRS with P(-5, 1), Q(-2,6), R(3, 7), and S(6, 4); d = ½

11. Translate ∆ABC A(3, 6), B(4,2), C(5, 6) right 4 and up 3 units. Then reflect the triangle across the y-axis. 12. You are given ∆ABC with A(1,4) B(-6,-2) C(4, -3). What rule transforms the triangle to give you the points A’(1, -4) B’(-6, 2) C’(4,3)? What type of transformation is it? 13. You are given pentagon JAROD with J(2, 0) A(4,2) R(6,0) O(6, -2) D(2,-2). What rule transforms the pentagon to the points J’(0,-2) A’(2, -4) R’(0, -6) O’(-2, -6) D’(-2, -2)? What type of transformation is it? 14. Perform these transformations in order on quad ABCD. A( -1, 1) B(0, 5) C(1, 2) D( 1, -1) (x, y) (3x, 3y) (x, y) (y, x) (x, y) (-x, -y) What are the final coordinates?


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Homework Answers:

Translation: Pages

Reflections: Pages


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Rotations: Pages Dilations HW: Pages


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Dilations: Page

Composition of Motion Part1 Page: 1) 5 2) 3 3) 5 4) 7 5) 1 6) 2 7) 1 8) 4 Part 2 Page: 1) (x, y) (y+2, x+4) 2) (x, y) (-3y, 3x) 3) (x, y) (-x+4, y-2)

4) (x, y) (y/3, -x/3) 5) (x, y) (x+4, -y+2) 6) (x, y ) (-2x, -2y)

7) (x, y) (y+2, x-4) 8) (x, y) (-x/2, -y/2)

Domain & Range:

1a. D: {1, 2, 5}, R: { -6, 5, 7} b. i. D: {3, 4, 7}, R: { -9, 2, 4} ii. D: {1, 2, 5}, R: { -7, -5, 6} iii. D: {-5, -2, -1}, R: { -6, 5, 7} iv. D: { -6, 5, 7}, R: {1, 2, 5} v. D: : { -6, 5, 7}, R{1, 2, 5} vi. D: {7, 14, 35}, R: { -42, 36, 49}

2a. D: [0, 3), R: (0, 4] b. i. D: [2, 5), R: (-3, 1] ii. D: [0, 3), R: [-4, 0) iii. D: (-3, 0], R: (0, 4] iv. D: [0, 4), R: (0, 3] v. D: (-3,0], R: (0,4] vi. D: [0, 21), R: (0, 28]

Unit Review: Pages

1) M’(-11, 0), N’(-6, -2), O’(-2, 3); (x, y)->(x-6, y-2) 2) P’(-30,6), Q’(-12, 36), R’(18, 42), S’(36, 24); (x, y)->(6x, 6y) 3) P’(0, 2), E’(-4, 6), N’(-8, -1), T’(-6, -3); (x, y)->(-x, y) 4) R’(4, 7), S’(-3, 5), T’(6, 2); (x, y)->(y, x) 5) F’(6, 8), G’(3, 1), H’(0, -4); (x, y)->(-x, -y) 6) A’(0, 0), B’ (4, 0), C’(4, -5), D’ (0, 5); (x, y)->(y, -x) 7) X’(2, -2), Y’(-4, -2), Z’(-1, 5); (x, y)->(-x, -y) 8) M’(-4, -16), N’(-12, -8), O’(-12,0), P’(-12, 16), Q’(-28, 8); (x, y)->(-4y, 4x) 9) M’(-5, 8), N’(0, 10), O’(4, 11); (x, y)->(x. y+6) 10) P’(-2.5, .5), Q’(-1,3), R’(1.5, 3.5), S’(3, 2); (x, y)->(0.5x, 0.5y) 11) A’(-9, 9), B’(-10, 5), C’(-11, 9); (x, y)->(-(x+6), y+3) 12) reflection over x-axis 13) rotation 90° CW 14) A’(-3, 3), B’(-5, 0), C’(-6, -3), D’ (3, -3)

Unit 1 Modeling with Geometry: Transformations€¦ · Common Core Math 2 Unit 1A Modeling with...

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