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Chapter 2: Transformational Geometry

Assignment Sheet

# Name Complete?

1 Functions Review

2 Video : Transformations

3 Generic Transformations and Isometries

4 Symmetry

5 Dilations and Translations

6 Lab: Reflections and Rotations

7 Reflections and Rotations

8 Video: Constructing Transformations

9 Investigating Transformations

10 Constructing Transformations

11 Video: Composite Transformations

12 Composite Transformations

13 Chapter Review

14 Chapter Test

Chapter 2 (October) 3

4 5

Chapter 1 Test

WR#3 Due

6

#1 Function

Review

HW: Video for

Sheet #2

7

No School For

Students

10

No School

Columbus Day

HW: Video for

Sheet #2

11

#3 Generic

Transformations

and Isometries

12

#4 Symmetry

WR#4 Due

13

#5 Dilations and

Translations

14

#6 Lab: Reflections

and Rotations

17

Skills Quiz/PSM

18

#7 Reflections and

Rotations

HW: Video for #8

19

#9 Investigating

Transformations

WR#5 Due 20

#10 Constructing

Transformations

HW: Video for #11

21

#12 Composite

Transformations

24

Skills Quiz/PSM

Progress Check 25

Due

#13 Chapter

Review

26

Chapter Test

WR#6 Due

27

28

Name __________________________________ Function Review

CC Geometry Chapter 2 Wksht #1 In algebra we studied functions extensively and during that time we learned how to solve for variables using function

notation. Let me show you a few examples to remind you.

What is the value of the

function 2( ) 3f x x when x = -2?

What is the value of the function ( ) 7f x x when x = 5?

What is the value of the

function 3

( )4

f x x when x = 12?

2

2

( ) 3

( 2) ( 2) 3

( 2) 4 3 1

f x x

f

f

( ) 7

(5) 5 7

(5) 12

f x x

f

f

3 3( ) ( ) (12)

4 4

36( ) 9

4

f x x f x

f x

When x = - 2, then y = 1 (-2,1) When x = 5, then y = 12 (5,12) When x = 12, then y = -9 (12,-9)

NYTS (Now You Try Some)

1. What is the value of the

function 2( ) 2f x x x when x = 4?

2. What is the value of the function ( ) 5 1f x x when x = 11?

3. What is the value of the

function 2

( )5

f x x when x = 5?

In all of these examples we were given the x value and then asked to solve for the y value (the value of the function). In

the next examples we will be given the y value (the value of the function) and then asked to work backwards to

determine the x value that would have produced that result. Look closely at these examples.

What is the value of x when ( ) 4 1f x x & ( ) 3f x ?

What is the value of x

when 2( ) 5f x x & ( ) 4f x ?

What is the value of x

when 5

( )12

xf x & ( ) 10f x ?

( ) 4 1

3 4 1

4 4

1

f x x

x

x

x

2

2

2

( ) 5

4 5

9 3

f x x

x

x x

5 5( ) 10

12 12

120 5 24

x xf x

x x

When y = - 3, then x = 1 (1,-3) When y = 4, then x = 3 ( 3,4) When y = 10, then x = 24 (24,10)

NYTS (Now You Try Some)

4. What is the value of x when ( ) 8 5f x x & ( ) 29f x ?

5. What is the value of x

when 3( ) 14f x x & ( ) 13f x ?

6. What is the value of x

when 1

( )3

xf x & ( ) 15f x ?

7. Given functions, ( ) 2 1f x x , 2( ) 2g x x x , and 2

( )5

xh x , determine value of the function for:

a) f(-5) = ______ b) g(-3) = ______ c) h(20) = ______

d) g(1) = ______ e) f(3

4

) = ______ f) h(

4

5)= ______

8. Given functions, ( )3

xr x , 2( ) 4s x x , and ( ) 4 8t x x , determine value of the function for:

a) ( ) 2r x x = ______ b) ( ) 64s x x = ______ c) ( ) 28t x x = ______

d) ( ) 12s x x = ______ e) 2

( )5

r x x = ______ f) ( ) 4t x x = ______

9. Using the function machine to determine the missing output or input values.

a) Input = -6 Output = ________

b) Input = 2

5

Output = ________

c) Input = ________ Output = -47

d) Input = ________ Output = 21

Name __________________________________ Video: Transformations

CC Geometry Chapter 2 Wksht #2

Transformations

What is a transformation?

Transformations as a Function:

Translation – Reflection –

Dilation – Rotation –

Invariant- Isometery-

Line Symmetry- Direct Isometry-

Point Symmetry-

𝐴(𝑥, 𝑦) − −−→ (2𝑦, 𝑥 − 3) 𝑇(𝑥, 𝑦) − −−→ (𝑥 + 3, 𝑦 − 6)

Name __________________________________ Generic Transformations and Isometries


1. Use the given coordinate rules to solve missing coordinates.

a) T (x,y) ------ > (x, y + 7) A (-4,9) A’ (_____ , _____) B (_____ , _____) B’ (5,0)

b) S (x,y) ------ > (-y, x) A (-4,9) A’ (_____ , _____) B (_____ , _____) B’ (9,7)

c) F (x,y) ------ > (5x, 3y) A (-4,9) A’ (_____ , _____) B (_____ , _____) B’ (-5,12)

d) G (x,y) ------ > (-x, -3x) A (-4,9) A’ (_____ , _____) B (_____ , _____) B’ (-8,-24)

e) H (x,y) ------ > (2x - 1, y - 3) A (-4,9) A’ (_____ , _____) B (_____ , _____) B’ (31,15)

f) P (x,y) ------ > (x + 3, 2y) A (-4,9) A’ (_____ , _____) B (_____ , _____) B’ (5,8)

2. Circle which of the following are isometric transformations.

Pre-Image a) b) c)

d) e) f)

3. Jane claims that any two circles are always isometric because the shape never changes. Is she correct?

YES or NO Explain your answer.

4. Determine if the pre-image and image are isometric and also which transformation produced the image.

PRE-IMAGE Circle Answer Circle Answer IMAGE

Isometry

Not Isometry

Rotation

Reflection Translation

Dilation Stretch Other

Isometry

Not Isometry

Rotation



Isometry

Not Isometry

Rotation



Isometry

Not Isometry

Rotation



Isometry

Not Isometry

Rotation



Isometry

Not Isometry

Rotation Reflection

Translation Dilation Stretch Other

Name __________________________________ Symmetry


1. Draw in the lines of symmetry for each of the shapes. If none, leave the diagram blank.

a) b) c) d)

e) f) g) h)

(Parallelogram)

(Regular Hexagon)

2. Use the diagrams from question #1 to determine the order and angle of rotation symmetry for the following

shapes. If none, write none.

a) Order = ____________

Angle = _____________

b) Order = ____________

Angle = _____________

c) Order = ____________

Angle = _____________

d) Order = ____________

Angle = _____________

e) Order = ____________

Angle = _____________

f) Order = ____________

Angle = _____________

g) Order = ____________

Angle = _____________

h) Order = ____________

Angle = _____________

3. Provided is half of a shape and the line of reflection.

4. Given a regular hexagon, how can you alter it so that instead of having six lines of reflection it only has two. Draw the altered hexagon and draw in the two lines of symmetry.

a) Complete drawing the shape. b) Using dashes marks to show equal sides – label each of the sides to show who is equal to who in the shape. c) Do the same for angles, label which angles are equal to each other in the shape using matching symbols. d) Finally, what do you notice about a shape that has one line of symmetry?

5. Given AB , determine the following.

a) Does it have point symmetry? ____________ b) How many lines of symmetry does it have? _____ c) Draw in the line(s) of symmetry. d) What is the unique name for the one of the lines of symmetry? 6) What is rotational symmetry order? _________

7. These two shapes have both rotational and reflectional symmetry. What do they have in common?

8. Determine the following symmetry characteristics for these REGULAR polygons.

Lines of Symmetry _________

Rotational Order __________







A

B

Name __________________________________ Dilations and Translations


Dilation

Examples:

1.) 3D (2, 6) 2.) 3

1D (6, 18)

3.) 4D (5,-2) 4.) 2D (1, 5)

5.) 4

1D (12,4) 6.) 5

1D (35, 80)

Translation

To find the image of a point under a translation, you add each coordinate to the given factor for x and y

a) 4,3T )4,3( yx b) 4,3 T )4,3( yx

Examples:

7.) 7,2T (2,6) 8.) 2,3T (6, 18)

9.) 5,4T (5,-2) 10.) 8,2T (1, 5)

11.) 9,3 T (12,4) 12.) 6,5 T (35, 80)

Practice

22.) Use the diagram to the right a rule for the Translation

Draw the image of the figure using the transformation shown.

23.) 24.)

2

1D

Name __________________________________ Lab: Reflections and Rotations


Materials: 2 Sheets of Graph Paper, 6 different colored markers, pen/pencil

Goals:

To be able to rotate and reflect on object with/without a “rule” on the coordinate plane

To understand the difference between the image and pre-image of an object

To create “rules” to reflect and Rotate and object on the coordinate plane

Rotations

Directions:

1. Plot and label the following 6 points (use a different color marker for each point).

A(2, 3) B (5, 7) C( 8, 2) D (1, 9) E( 2, 7) F(4, 2)

2. Rotate your paper 90o by turning it to the left one turn. (FYI: Geometrical notation for this is R90) Once you

have done this and are looking at your transformed points, fill out the chart below based on your NEW points

given the NEW orientation of you graph. (I started the first row for you)

Pre-Image (Starting Point) Image (New point)

A (2, 3)

A (-3, 2)

B

C

D

E

F

3. Do you see a pattern between the Pre-Image points and the Image points? Could you come up with a rule to

Rotate a coordinate 90o using x and y?

4. Rotate your paper 180o by turning it to the left one turn. If you already moved it back to the original

position, you will have to turn it to the left two turns. (FYI: Geometrical notation for this is R180) Once you have

done this and are looking at your transformed points, fill out the chart below based on your NEW points given

the NEW orientation of you graph. (I started the first row for you)


A (2, 3)

A (-2,-3)

B

C

D

E

F



6. Rotate your paper 270o by turning it to the left one turn. If you already moved it back to the original

position, you will have to turn it to the left three turns. (FYI: Geometrical notation for this is R270) Once you

have done this and are looking at your transformed points, fill out the chart below based on your NEW points

given the NEW orientation of you graph. (I started the first row for you)


A (2, 3)

A (3,-2)

B

C

D

E

F



8. What do you think a Rotation of 360o would be the same as?

9. What do you think a Rotation of -90o would be the same as?

Reflections

Directions:

1. On the other graph paper, plot and label the following points (use a different color marker for each point).

A(1, 0) B (3, 1) C( 5, 2) D (8, 4) E( 4, 3) F(6, 5)

2. Reflect the point over the x-axis by folding the piece of paper at the x-axis. (FYI: Geometrical notation for

this is rx-axis) Once you have done this and are looking at your transformed points, fill out the chart below based

on your NEW points given the NEW orientation of you graph. (I started a row for you).


A (1,0)

B

C

D (8, 4)

D (8, -4)

E

F


reflect a coordinate over the x-axis?

4. Reflect the point over the y-axis by folding the piece of paper at the y-axis make sure you have opened your

graph paper back up first. (FYI: Geometrical notation for this is ry-axis) Once you have done this and are looking

at your transformed points, fill out the chart below based on your NEW points given the NEW orientation of

you graph. (I started a row for you).


A (1,0)

B

C

D (8, 4)

D (-8, 4)

E

F


reflect a coordinate over the x-axis?

6. The line y=x contains all coordinates where x and y are the same ex (-4, -4), (-3,-3), (-2, -2), (-1, -1), (0, 0),

(1, 1), (2, 2), (3,3), (4,4) Graph this line using a PENCIL and a STRAIGHTEDGE.

Reflect the points over the line y=x by folding the piece of paper at the line you drew make sure you have

opened your graph paper back up first. (FYI: Geometrical notation for this is ry=x) Once you have done this and

are looking at your transformed points, fill out the chart below based on your NEW points given the NEW

orientation of you graph. (I started a row for you).


A (1,0)

B

C

D (8, 4)

D (4, 8)

E

F


reflect a coordinate over the line y=x?

8. The line y=-x contains all coordinates where x and y are the same but one is negative ex (-4, 4), (-3,3), (-2, 2),

(-1, 1), (0, 0), (1, -1), (2, -2), (3,-3), (4,-4) Graph this line using a PENCIL and a STRAIGHTEDGE.

Reflect the points over the line y=-x by folding the piece of paper at the line you drew make sure you have

opened your graph paper back up first. (FYI: Geometrical notation for this is ry=-x) Once you have done this and

are looking at your transformed points, fill out the chart below based on your NEW points given the NEW

orientation of you graph. (I started a row for you).


A (1,0)

B

C

D (8, 4)

D (-4, -8)

E

F


reflect a coordinate over the line y=-x?

Name __________________________________ Reflections and Rotations


1. Determine the line of reflection for the following pre-image and images.

a) b) c)

d) e) f)

2. Determine the pre-image coordinates, then reflect it, and determine the image coordinates.

a) A = ( ____ , ____) ( )x axisr A A ‘ = ( ____ , ____)

b) B = ( ____ , ____) ( )y axisr B B ‘ = ( ____ , ____)

c) C = ( ____ , ____) ( )mr C C ‘ = ( ____ , ____)

d) D = ( ____ , ____) ( )x axisr D D ‘ = ( ____ , ____)

e) E = ( ____ , ____) ( )x axisr E E ‘ = ( ____ , ____)

f) F = ( ____ , ____) ( )nr F F ‘ = ( ____ , ____)

g) G = ( ____ , ____) ( )y axisr G G ‘ = ( ____ , ____)

n

m

A

B

C

D

E

F

G

3. Circle the center of rotation for the following pre-image and images.

a) A rotation of 90 b) A rotation of 180 c) A rotation of 180

4. Determine the pre-image coordinates, then rotate it, and determine the image coordinates. Patty paper will help

determine the image coordinates. (Patty paper might be helpful here.)

,90 ( )OR ABC

a) A = ( ____ , ____) ,90 ( )OR ABC A ‘ = ( ____ , ____)

b) B = ( ____ , ____) ,90 ( )OR ABC B ‘ = ( ____ , ____)

c) C = ( ____ , ____) ,90 ( )OR ABC C ‘ = ( ____ , ____)

,90 ( )OR DFE

d) D = ( ____ , ____) ,90 ( )OR DFE D ‘ = ( ____ , ____)

e) E = ( ____ , ____) ,90 ( )OR DFE E ‘ = ( ____ , ____)

f) F = ( ____ , ____) ,90 ( )OR DFE F ‘ = ( ____ , ____)

5. Determine the name of the point that meets the given conditions.

a) ,60 ( )GR A ________ b) ,180 ( )GR B ________

c) ,300 ( )GR D ________ d) , 120 (______)GR B

e) ,240 ( )GR E ________ f) , 240 ( )GR F ________

g) ,60 ( )AR B ________ h) ,120 ( )CR D ________

A = A'

B

B'

E'B'

B

E

D = D'

B'

E'

B

E

A

C

B

D

E

F

O

A

B

C

A'

Name __________________________________ Video: Constructing Transformations


1. Constructing a reflection using a compass and straightedge.

2. Constructing a translation using a compass and straightedge.

(1) Translate ABC by Vector 'AA . (2) Place the compass pointer on point A and

measure the length of 'AA . (3) Using the compass length of AA’, place the compass pointer at point B and create an arc in the general direction of the translation. Do the same thing from point C. (4) Measure the length of AB. Place the compass pointer at A’ and create an arc in the general direction of the arc from B. The intersection of these two arcs is B’. (5) Measure the length of AC. Place the compass pointer at A’ and create an arc in the general direction of the arc from C. The intersection of these two arcs is C’. (6) Use the straightedge to form the translated triangle.

m

B

A

(1)Placing the compass pointer at point A make a circle of any radius as long as it intersects line m twice. In this case, name them points C and D.

(2) Leaving the compass radius the same - place the compass pointer at C and make an arc on the opposite side of A. Do that as well from D. The intersection of these two arcs is A’.

(3) Placing the compass pointer at B make a circle of any radius as long as it intersects line m twice. In this case, points F and G.

(4) Leaving the compass radius the same - place the compass pointer at F and make an arc on the opposite side of B. Do that as well from G. The intersection of these two arcs is B’

(5) Use the straightedge to create ' 'A B .

Name __________________________________ Investigating Transformations


1. Which transformation has taken place?

a) ___________________ b) ___________________ c) ___________________ d) ___________________

2. Complete the chart.

Relationship between pre-image and image

ROTATION REFLECTION TRANSLATION

Distances

SAME OR DIFFERENT SAME OR DIFFERENT SAME OR DIFFERENT

Orientation

SAME OR DIFFERENT SAME OR DIFFERENT SAME OR DIFFERENT

Special Points

3. Given that ABC was mapped to A’B’C’ using a single transformation.

a) Why couldn’t this mapping have resulted by a single translation? b) What transformation must have mapped these two triangles? Explain your answer.

4. Given that ABC was mapped to A’B’C’ using a single transformation.

a) Why couldn’t this mapping have resulted by a single reflection? b) What transformation must have mapped these two triangles? Explain your answer.

B'

D'C'

C

D

B

D'

C'C

D

B

B'B'

D'

C'

C

D

B

D'

F'

E'E

F

D

C'

B'

A'A

B

C

A'

C'

B'B

C

A

5. ABC is congruent to A’B’C’. A student tries to determine which of these single transformations mapped ABC

onto A’B’C’. She concludes that a reflection had to be involved and more than one transformation had to map these on two triangles.

a) How can she conclude that a reflection was involved?

b) How can she conclude that this wasn’t just a single reflection?

6. Determine the location of Point A,

a) after a reflection A = A’, where was point A? __________________________________

b) after a rotation of 27 A = A’, where was point A? _________________________________

7. After a reflection AA’ = 24 cm, how far was A away from the line of reflection? ______________

8. If after a reflection A = A’ and BB’ = 6 cm. What is the relationship between BAB’ and the line of reflection. Draw

a diagram.

9. The distance from point A to the line of reflection is 10 cm, and the distance from point B to the line of reflection is

also 10 cm. Jeffrey concludes that B is the image of A under a reflection. What do you think of this conclusion?

10 . BC was translated by the arrow making ' 'BC B C and || ' 'BC B C .

a) What other segments in the diagram are congruent? ______________ b) What other segments in the diagram are parallel? _______________

C'

B'

A'

A

B

C

C'

C

B

B'

Name __________________________________ Constructing Transformations

CC Geometry Chapter 2 Wksht #10 1. Use a compass and a straightedge to construct the following reflections.

rm

m

A

B

C

rm

mA

B

rm

mA

B

C

rm

m

A

B

C

2. Determine the Line of Reflection

a) In trying to find the line of reflection you need to work backwards through the definition of a reflection.

Construct the line of reflection of ABC &

A’C’B’ How do you know that this is a reflection and not a rotation?

b) What about this transformation tells you that it must be a reflection and not something else? Construct the line of reflection of

ABC & A’C’B’.

c) What in this diagram gives us a clue about where the line of reflection is?

Construct the line of reflection of ABC & A’C’B’.

A'

B'

C'

C B

A

A'

B'

C'

C B

A

A'

B'

C'

C

B

A

TIP…. If you are trying to find the center of a circle we use the perpendicular bisector to help us.

A circle with no center Perform the perpendicular

bisector of any two points on the circle. This line passes through the center.

Perform it a second time and the intersection must be the center because both perpendicular bisectors split the circle in half.

Now you have found the center of the circle.

4. a) Construct the center of rotation and determine the angle of rotation. (Use a protractor to measure the angle size)

b) Construct the center of rotation of BCD & B’C’D’. Use the tip above…. Apply it to find the CENTER of rotation.

c) Construct the center of rotation of ABC & A’B’C and determine the angle of rotation. (Use a protractor to measure the angle size) Use the tip above…. Apply it to find the CENTER of rotation.

A

B

A

B

C'

B'

A

B

C

D'B'

C'

C

B

D

C'

B'

A'

A

B

C

5. Use a compass and a straightedge to construct the following translations.

'( )

AAT ABC

'( )

BBT ABC

'( )

AAT ABC AND THEN ( ' ' ')mr A B C

A

B

C

A'

A

B

C

B'm

A

B

C

A'

Name __________________________________ Video: Composite Transformations


Rules

Dilation Translation Reflection Rotation

Compositions Example:

What is the image of R (3, -2) under the composition below?

Example:

Given triangle ABC with E(-2,1) A(0, -1) and M(-1, -3) state the coordinates of the image of triangle ABC

under the composition . (The use of the grid is optional)

Example:

Given triangle ABC with A(2, 3) B(-2, 4) and C (-1, 1) state the

coordinates of the image of triangle ABC under the composition

. (The use of the grid is optional)

290 DR

1802 Rry

4,3Tr axisy

)5,3(2D )5,3(3,2 T )5,3(axisxr

)5,3(axisyr

)5,3(xyr

)5,3(xyr

)5,3(270 R

)5,3(180 R

)5,3(90 R

http://www.google.com/url?sa=i&source=images&cd=&cad=rja&docid=6RPEjJentpQNrM&tbnid=Khql0lrrMy_nDM:&ved=0CAgQjRwwAA&url=http://mathbits.com/MathBits/StudentResources/GraphPaper/GraphPaper.htm&ei=OWNNUt_FDIv-8QSsloGQBg&psig=AFQjCNHRfA6qs6eAE5g_5Qx2ofPSWhhmCw&ust=1380889785275149

http://www.google.com/url?sa=i&source=images&cd=&cad=rja&docid=6RPEjJentpQNrM&tbnid=Khql0lrrMy_nDM:&ved=0CAgQjRwwAA&url=http://mathbits.com/MathBits/StudentResources/GraphPaper/GraphPaper.htm&ei=OWNNUt_FDIv-8QSsloGQBg&psig=AFQjCNHRfA6qs6eAE5g_5Qx2ofPSWhhmCw&ust=1380889785275149

Name __________________________________ Composite Transformations


COMPOSITE TRANSFORMATIONS

DOES ORDER MATTER – Use the composite transformation to plot A’B’C’ and A’’B’’C’’

1a) 3,5 ( )y axisT r ABC b) 3,5 ( )y axisr T ABC

c) Did doing the transformations in a different order matter? Explain why?

2a) ,90 ( )x axis Or R ABC b) ,90 ( )O x axisR r ABC

c) Did doing the transformations in a different order matter? Explain why?

A (6,-1)

B (5,-7)

C (3,-4)

A (6,-1)

B (5,-7)

C (3,-4)

A (1,8)

B (4,7)

C (1,3)

A (1,8)

B (4,7)

C (1,3)

Name __________________________________ Chapter Review


Vocabulary:

Reflection Rotation Translation Transformation Dilation

Isometry Direct Isometry Invariant

1. What is the value of the function, ( ) 3 1f x x when x = -3?

A) 8 B) - 10 C) -8 D) - 1

1. _____

2. Given the function, ( )4

xf x , what is the value of x when ( ) 16f x ?

A) x = 4 B) x = -4 C) x = 64 D) x = 8

2. _____

3. A student places x = 3 into the function, ( ) 5 7f x x and gets ( ) 8f x . ( ) 8f x is the:

A) Input B) Output C) Domain D) Maximum

3. _____

6. If you have a rotational symmetry angle of 18, then your order is: A) 2 B) 5 C) 10 D) 20

6. _____

7. Which of the following has exactly one line of symmetry? A) A Rectangle B) An Isosceles Trapezoid C) A Rhombus D) A Parallelogram

7. _____

8. This shape has: A) Only Rotational Symmetry B) Only Reflectional Symmetry

C) Both Rotational & Reflectional Symmetries D) Neither symmetry

8. _____

9. ABC is reflected to create image A’B’C’. Which statement is always true?

A) AB || ' 'A B B) 'AA 'BB C) AB ' 'A B D) 'AA || 'BB

9. _____

11. Which transformation changes the orientation of the shape? A) Rotation B) Dilation C) Translation D) Reflection

11. _____

Determine whether the following are (T)rue or (F)alse.

13. ( , ) ( 5, )T x y x y is an isometric transformation. T or F

14. ( , ) (3 , 2)T x y x y is an isometric transformation. T or F

15. If a shape has a rotational order of 1, then it has NO rotational symmetry. T or F

16. A rotational symmetry of order 2 means that the angle of the order is 90. T or F

17. If point A is 2.5 cm from the line of reflection, then AA’ = 5 cm. T or F

18. A rotation of 180 reverses the orientation of the shape. T or F

19. When a rotation of 80 about point T is performed, all points in the plane move. T or F

20. The isometric transformations are rotation, reflection, dilation and translation. T or F

21.Given coordinate rule 2( , ) ( , 5)T x y x

determine the image of A(-2,2)?

22. Given coordinate rule, ( , ) ( 2, 6)T x y x y determine the pre-image of A’(-2,2)?

ABC is reflected over line g to create the image A’B’C’. What is the relationship between 'AA , 'BB and 'CC ?

26. What are the coordinate rules for the given transformations? REFLECTION RULES ROTATION RULES

( , ) (______, ______)y axisR x y ,90 ( , ) (_____, _____)OR x y

( , ) (______, ______)x axisR x y ,180 ( , ) (_____, _____)OR x y

( , ) (______, ______)y xR x y ,270 ( , ) (_____, _____)OR x y

What are the characteristics of the given transformations?

CHARACTERISTIC REFLECTION ROTATION TRANSLATION

ISOMETRIC? YES OR NO YES OR NO YES OR NO

DISTANCES (all points move the same distance)

YES OR NO YES OR NO YES OR NO

OREINTATION? SAME OR REVERSE SAME OR REVERSE SAME OR REVERSE

CAN A = A’? YES OR NO YES OR NO YES OR NO

27. Determine whether the following are (T)rue or (F)alse.

If a translation maps A (-3,5) to A’ (3, 5), then T(x,y) ------> (x – 6,y) would be the rule. T or F

F (x,y) -------> (x + 3,y) is a translation of 3 units to the right. T or F

A rotation of 270about the origin maps A (1,-2) to A’ (-2,-1) T or F

,180O x axis y axisR R R T or F

Three reflections over parallel lines could also be described as a single translation. T or F

A composite transformation of a rotation followed by translation reverses the

orientation of the shape. T or F

A translation of 2 right and 5 down followed by a reflection on the x axis is 2, 5 x axisT R

T or F

A double reflection over y = 3 followed by y = 4, translates all points up 2 units. T or F

A double reflection over y = -3 followed by y = -1, translates all points up 4 units. T or F

11 6 0,10y yR R T T or F

28. Perform the following on the

grid.

a) ,90 ( )MR NOPQ

b) ,180 ( )FR GHI

c) ( )AB

R CDE

d) 3,2 ( )T JKL

6

4

2

2

4

10 5 5

B

A

D

C

F

I

H

G

L

K

O

PQ

N

ME

J

29. Use your rules to solve these.

a)

(5,4) '(_______, _______)x axisR A A

b) ( 5,1) ''(______, ______)y axis x axisR R A A

c)

(_______, _______) ''(4, 3)x axis y axisR R A A d) 3,5 (_______, _______) '(9, 3)T A A

e)

2, 1 (5,3) ''(_______, _______)y axisT R A A

f)

( 1,6) '(_______, _______)x axisR A A

g)

,90 (3,2) '(_______, _______)OR A A

h)

,90 (_______, _______) '(8,3)OR A A

30. Construct the following ( )mR ABC and Center of Rotation for Triangle DEF

m

C

B

A

chapter 2: transformational geometry assignment sheet€¦ · chapter 2 (october) 3 4 5 chapter 1...

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