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Name________________________ Date _____ Per. _____ Teacher

Chapter 12

Transformations:

Shapes in Motion

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Table of Contents

Reflections – Day 1 ……………………………………………..…………….. Page 3

Translations – Day 2 ……………….……….…………….……..…………….. Page 10

Rotations – Day 3…………………………………………..………………….. Page 17

Dilations – Day 4 ……………………………………………………….….….. Page 24

Symmetry – Day 5 ………………………………………..……..…………….. Page 33

Glide Reflections – Day 6……………………………………………….…….. Page 38

Compositions – Day 7………………………………………………..………….. Page 44

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Reflections – Day 1

An Introduction to Transformations

Image - _______________________________________________________

Preimage - ____________________________________________________

Isometry - ____________________________________________________

_____________________________________________________________

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Reflections

Reflection-

Reflection Over the X-Axis a. Graph triangle PQR with vertices P(-3, 4), Q(4, 2), and R(-1, 1). Then graph the image of

triangle PQR after a reflection over the x-axis. Write the coordinates of its vertices.

P(-3, 4) Pl________

Q(4, 2) Ql_______

R(-1, 1) Rl________

Rule

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Reflection Over the Y-Axis b. Graph quadrilateral ABCD with vertices A(-4, 1), B(-2, 3), C(0, -3) and D(-3, -2). Then graph the

image of ABCD after a reflection over the y-axis. Write the coordinates of its vertices.

A(-4, 1) Al________

B(-2, 3) Bl________

C(0, -3) Cl________

D(-3, -2) Dl________

Rule

Reflection Over the line y = x.

c. Graph trapezoid ABCD with vertices A(-4, 7), B(-1, 7), C(0, 5), and D(-5, 5). Then graph the

image of ABCD after a reflection over the line y = x. Write the coordinates of the new vertices

Rule

A(-4, 7) Al________

B(-1, 7) Bl________

C(0, 5) Cl_______

D(-5, 5) Dl________

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Reflection over a Horizontal or Vertical Line d. Graph triangle ABC with vertices A(-4, 1), B(-1, 1), and C(-3, 4). Then graph the image of

ABC after a reflection over the line y = -3. Write the coordinates of the new vertices.

Identifying a Reflection Write a rule to describe each transformation.

a. b.

A(-4, 1) Al________

B(-1, 1) Bl________

C(-3, 4) Cl________

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Summary

Find the coordinates of the vertices for the reflection images of the triangle in the x- axis,

y-axis, and the line y = x.

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Homework

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Translations – Day 2

Warm - Up

1.

2.

Translation- ___________________________________________________

_____________________________________________________________

_____________________________________________________________

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1) Triangle DEF is a translation of triangle ABC.

Use the diagram to write a rule for the translation of triangle ABC to Triangle DEF.

2) Pentagon ABCDE is drawn on the grid below.

On the grid, draw a translation of pentagon ABCDE using the rule T3,-5.

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3) Pentagon ABCDE is plotted on the grid below.

On the grid, draw the translation of pentagon ABCDE using the rule T-4,3. Label the

translated figure A’B’C’D’E’.

4.

5.

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Summary

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Homework

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Rotations – Day 3

Warm - Up

1.

2.

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Example 1: Graph triangle XYZ with vertices X(2, 2), Y(4, 3), and Z(3, 0).

Then graph the image of triangle XYZ after a rotation 90o counterclockwise about the

origin, and write the coordinates of its vertices.

X(2, 2) Xl( , )

Y(4, 3) Yl( , )

Z(3, 0) Zl( , )

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Example 2: Graph trapezoid ABCD with vertices A(1, 3), B(4, 4), C(4, 0), and

D(1, 1). Then graph the image of trapezoid ABCD after a 180o rotation about

the origin, and write the coordinates of its vertices.

Example 3: Graph polygon TUVW with vertices T(2, -4), U(3, -1), V(-1, 0), and

W(-2, -3). Then graph the image of polygon TUVW after a 270o rotation, and

write the coordinates of its vertices.

A(1, 3) Al ( , )

B(4, 4) Bl ( , )

C(4, 0) Cl ( , )

D(1, 1) Dl ( , )

T(2, -4) Tl ( , )

U(3, -1) Ul ( , )

V(-1, 0) Vl ( , )

W(-2, -3) Wl ( , )

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Identifying a Rotation Write a rule to describe each transformation.

a.

b.

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Summary

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Homework

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Dilations – Day 4 SWBAT: Identify and Draw Dilations

Warm – Up

1. 2.

4. What are the coordinates of the image

(2,-5) after a counterclockwise rotation

of 270˚ about the origin?

a. (-2, 5)

b. (2, 5)

c. (-5, -2)

d. (5, -2)

Dilation - _____________________________________________________

_____________________________________________________________

Scale factor- ___________________________________________________

_____________________________________________________________

Enlargement - _________________________________________________

_____________________________________________________________

Reduction - ___________________________________________________

_____________________________________________________________

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To find the image of a point under a dilation, you multiply by the scale factor.

a) D4 (x,y) (4x,4y) b) D6

1(x,y) ( Yx

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1,

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1)

Example- Find a) D2(3,4)

b)

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D (6,9)

Example 1-Enlargement

Graph triangle PQR with vertices P(-1, 1), Q(4, 1), and R(-1, 3). Then Graph its image

triangle P’Q’R’ after a dilation with a scale factor of 2.

P(-1, 1) P’________

Q(4, 1) Q’_______

R(-1, 3) R’________

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Example 2-Reduciton

Graph quadrilateral EFGH with vertices E(-6, 4), F(-4, 8), G(4, 2), and H(-2, -4). Then

graph the image of EFGH after a dilation with a scale factor of ½ .

Example 3-Determining the Scale Factor

Graph triangle ABC with vertices A(-4, 6), B(-2, 4), and C(-8, 4). Then graph the image

of ABC after a dilation triangle A’B’C’ with vertices Al(-2, 3), Bl(-1, 2), and Cl(-4, 2).

Find the scale factor of the dilation and classify as an enlargement or a reduction.

E(-6, 4) E’________

F(-4, 8) F’_______

G(4, 2) G’_______

H(-2, -4) H’________

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You Try!!!

1. Graph triangle ABC with vertices A(-2, 1), B(3, 1), and C(-3, 3). Then graph the

image of ABC after a after a dilation with a scale factor of 3.

2. Graph quadrilateral EFGH with vertices E(-6, 4), F(-4, 8), G(4, 2), and H(-2, -4).

Then graph the image of quadrilateral EFGH after a dilation with a scale factor of2

3.

3. Triangle ABC with vertices A(-3, 6), B(-6, 9), and C(-9, -3). The graph of the image of

ABC after a dilation triangle A’B’C’ with vertices Al(-2, 4), Bl(-4, 6), and Cl(-6, -2).

Find the scale factor of the dilation and classify as an enlargement or a reduction.

A(-2, 1) Al________

B(3, 1) Bl________

C(-3, 3) Cl________

E(-6, 4) E’________

F(-4, 8) F’_______

G(4, 2) G’_______

H(-2, -4) H’________

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Name: _________________________ Per.: ______ Date: _________ Transformation Review – Homework

1) Which transformation is shown in the accompanying diagram?

a) Reflection

b) Rotation

c) Translation

d) Dilation

2) A translation maps (x,y) to (x – 5, y + 3). In which quadrant does the point (-3, -2) lie under the

same translation?

a) I

b) II

c) III

d) IV

3) A translation moves point B (-5, 3) to point B’ (2, 1). What is the image of (x,y) under this

translation?

a) (x + 7, y – 2)

b) (x + 7, y + 2)

c) (x – 3, y – 2)

d) (x – 3, y + 2)

4) Which transformation for ∆RST is shown in the diagram below?

a) Line reflection

b) Translation

c) Rotation

d) Dilation

5) What is the image of (1, -3) when reflected about the y-axis?

a) (-1, 3)

b) (3, -1)

c) (-3, -1)

d) (-1, -3)

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6) If the point (5,1) is reflected in the x-axis, the image is:

a) (-5, 1)

b) (-5,-1)

c) (5, 1)

d) (5, -1)

7) What are the coordinates of P’, the image of P(-1,4) after a reflection in the line x = 2?

a) (4,1)

b) (-1,1)

c) (0,4)

d) (5,4)

8) In the accompanying diagram of right triangle ABC with the right angle C, line l is drawn

through C and is parallel to AB .

If ∆ABC is reflected in line l, forming the image ∆A’B’C’, which statement is not true?

a) C and C’ are the same point

b) m<ABC = m<A’B’C’

c) The area of ∆A’B’C’ is twice the area of ∆ABC.

d) Line l is equidistant from A and A’.

9) Point P’ (-6,-4) is the image of point P (-2, 3) under translation T. What is the image of (5,-1)

under the same translation?

a) (9,6)

b) (1,-8)

c) (-1,-5)

d) (3,2)

10) What are the coordinates of the image (2,-5) after a counterclockwise rotation of 90˚ about the

origin?

a) (-2, 5)

b) (2, 5)

c) (-5, -2)

d) (5, 2)

11) The enlargement of a photograph is an example of a:

a) Line reflection

b) Translation

c) Dilation

d) Rotation

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12) Which transformation is represented by the illustration?

a) Reflection

b) Dilation

c) Translation

d) Rotation

13) What is the image of point (4,-2) after a dilation of 3?

a) (4/3, -2/3)

b) (12, -6)

c) (7, 1)

d) (1, -5)

14) The image of P(6, -9) after a dilation with respect to the origin is (4, -6). What is the constant of

dilation?

a) 1

3

b) 2

3

c) 3

2

d) -2

15) In which quadrant will the image of A (4, -2) lie after dilation D-2?

a) I

b) II

c) III

d) IV

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Part Two:

16.

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Symmetry – Day 5

Warm - up

1.

2.

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Homework

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Glide Reflections – Day 6

Warm – Up

1.

2.

Which rotation about point O maps B to D? _______

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The symbol for a composition of transformations is an open circle.

The notation is read as a reflection in the x-axis following a translation of

(x+3, y+4). Be careful!!! The process is done in reverse!!

You may see various notations which represent a composition of transformations:

could also be indicated by

Identifying Glide Reflections

1.

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2)

3) Is T0, 5 ry-axis a glide reflection?

4) Is T7, 0 rx-axis a glide reflection?

5) Is T3,3 ry=x a glide reflection?

6) Is T4,-1 ry-axis a glide reflection?

7) Is T-2, 8 rx-axis a glide reflection?

Practice Problem #8

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Practice Problem #9

Given: ABC: A (-4, 5), B (-6, 7), C (-8, 3)

Practice Problem #10

Given: ABC: A (5, 1), B (7, 4), C (9, 1)

T-5,-4 rx-axis

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Homework

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Compositions (More Practice) – Day 7

When two or more transformations are combined to form a new transformation, the result

is called a composition of transformations. In a composition, the first transformation

produces an image upon which the second transformation is then performed.

The symbol for a composition of transformations is an open circle.

The notation is read as a reflection in the x-axis following a translation of

(x+3, y+4). Be careful!!! The process is done in reverse!!

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Try it Problems

1. The transformation (x, y) → (2x + 4, 2y + 1) is the composition of what two transformations?

2.

3.

4.

5.

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Homework: Transformations Review

1) In the accompanying diagram, K is the image of A after a translation. Under the same translation,

which point is the image of J?

2) A translation moves A (-1, 3) to A’ (-3, 7). What are the coordinates of B’, the image of B(5,-3) under

the same translation?

3) Find the coordinates of P’, the image of P (-3, 4) under the translation T4,1.

4) Translation T maps point (2, 6) to point (4, -1). What is the image of point (-1, 3) under translation T?

5) Which graph shows a reflection ABC in the x-axis?

6)

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7) Find the coordinates of P’, the image of P(3, -1) under the transformations (x,y) (-y, -x).

8) What is the image of (6, 5) under a counterclockwise rotation of 180˚?

9) If point P (3, -2) is rotated 90˚ about the origin, what is the image of P?

10) Which transformation does not preserve size?

11) The image of (-2, 6) after a dilation with respect to the origin is (-10, 30). What is the constant of

dilation?

12) Which transformation for letter M is shown in the accompanying diagram?

13) If a dilation maps (-3, 2) to (x, 8), what is the value of x?

14) If the coordinates of point A are (–2,3), what is the image of A under r Dy axis 3 ?

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15) On the accompanying grid, graph and label AB , where A is (0,5) and B is (2,0). Under

the transformation ),(ABrr axisyaxisx A maps to A , and B maps to B . Graph and

label A B .

What single transformation would map AB to A B ?

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22.

In 16 - 21: a. Find the image of P(5, -3) under each of the given transformations.

16. rx-axis 17. R180 18. R90

19. T0,3 20. rx-axis T2,2 21. rx-axis ry=x

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23.