7-7 Transformations

Course 3

Warm Up

Problem of the Day

Lesson Presentation

Warm Up

Course 3

7-7 Transformations

Determine if the following sets of points form a parallelogram.

1. (–3, 0), (1, 4), (6, 0), (2, –4)

2. (1, 2), (–2, 2), (–2, 1), (1, –2)

3. (2, 3), (–3, 1), (1, –4), (6, –2)

yes

no

yes

Problem of the DayHow can you move just one number to a different triangle to make the sum of the numbers in each triangle equal? (Hint: There do not have to be exactly 3 numbers in each triangle.)

Course 3

7-7 Transformations

Move the 9 to the first triangle.

Learn to transform plane figures using translations, rotations, and reflections.

Course 3

7-7 Transformations

Course 3

7-7 Transformations

Vocabulary

transformation

translation

rotation

center of rotation

reflection

image

Course 3

7-7 Transformations

When you are on an amusement park ride,you are undergoing a transformation. Ferris wheels and merry-go-rounds are rotations. Free fall rides and water slides are translations. Translations, rotations, and reflections are type of transformations.

Course 3

7-7 Transformations

The resulting figure or image, of a translation, rotation or reflection is congruent to the original figure.

Course 3

7-7 Transformations

Additional Example 1: Identifying Transformations

Identify each as a translation, rotation, reflection, or none of these.

A. B.

reflection rotation

A’ is read “A prime”. The point A is the image of point A.

Reading Math

Course 3

7-7 Transformations

Additional Example 1: Identifying Transformations

Identify each as a translation, rotation, reflection, or none of these.

C. D.

none of the these translation

Course 3

7-7 Transformations

Check It Out: Example 1

Identify each as a translation, rotation, reflection, or none of these.

A

B C

A. B. A B

CD

A’ B’

C’D’

translation reflection

A’

B’ C’

Course 3

7-7 Transformations

Identify each as a translation, rotation, reflection, or none of these.

BC

DE

F

C. D.

A

A’

B’C’

D’

F’

E’

rotation none of these

Check It Out: Example 1

Course 3

7-7 Transformations

Additional Example 2A: Graphing Transformations

Draw the image of the triangle with vertices A(1, 1), B(2, -2), and C(5, 0) after each transformation.

A 180° counterclockwise rotation around (0, 0)

A

B

C A’

B’

C’x

y

–2

2

0 2 4 –2 –4

Course 3

7-7 Transformations

Additional Example 2B: Graphing Transformations

Draw the image of the triangle with vertices A(1, 1), B(2, -2), and C(5, 0) after each transformation.

A reflection across the y-axis

A

B

C

B’

A’

C’x

y

–2

2

0 2 4 –2 –4

Course 3

7-7 Transformations

Check It Out: Example 2A

X

Y

Z

X’

Y’

Z’x

y

–2

2

0 2 4 –2 –4

Draw the image of the triangle with vertices A(1, 2), B(2, –3), and Z(7, 0) after each transformation.

A 180° counterclockwise rotation around (0, 0)

Course 3

7-7 Transformations

Check It Out: Example 2A

X

Y

Z

Y’

X’

Z’x

y

–2

2

0 2 4 –2 –4

Draw the image of the triangle with vertices A(1, 2), B(2, -3), and Z(7, 0) after each transformation.

A reflection across the y-axis

Course 3

7-7 Transformations

Additional Example 3A: Describing Graphs of Transformations

Rectangle HIJK has vertices H(0, 2), I(4, 2), J(4, 4), and K(0, 4). Find the coordinates of the image of the indicated point after each transformation.

Translation 2 t units up, point H

x

y

–2 2

H I

K JH’ I’

K’ J’

H I

K JH’(0, 4)

Course 3

7-7 Transformations

Additional Example 3B: Describing Graphs of Transformations

Rectangle HIJK has vertices H(0, 2), I(4, 2), J(4, 4), and K(0, 4). Find the coordinates of the image of the indicated point after each transformation.

90° rotation around (0, 0), point I

x

y

–2 2

H I

K J

‘H

‘I

‘K

‘J

I’(2, –4)

Course 3

7-7 Transformations

Check It Out: Example 3AParallelogram ABCD has vertices A(1, –2), B(3, 2), C(7, 3), and D(6, –1). Find the coordinates of the images of the indicated point after each transformation.

180° clockwise rotation around (0, 0), point A

x

y

–2

2

A

BC

DB’

A’

C’

D’

A’(–1, 2)

Course 3

7-7 Transformations

Check It Out: Example 3B

Parallelogram ABCD has vertices A(1, –2), B(3, 2), C(7, 3), and D(6, –1). Find the coordinates of the images of the indicated point after each transformation.

Translation 10 units left, point C

x

y

–2

2

A

BC

D

C’(-3, 3)

A

BC

D

Course 3

7-7 Transformations

Lesson Quiz: Part IGiven the coordinates for the vertices of each pair of quadrilaterals, determine whether each pair represents a translation, rotation, reflection, or none of these.

1. (2, 2), (4, 0), (3, 5), (6, 4)

and

(3, –1), (5, –3), (4, 2), (7, 1)

2. (2, 3), (5, 5), (1, –2), (5, –4)

and

(–2, 3), (–5, 5), (–1, –2), (–5, –4)

translation

reflection

Course 3

7-7 Transformations

Given the coordinates for the vertices of each pair of quadrilaterals, determine whether each pair represents a translation, rotation, reflection, or none of these.

3. (1, 3), (–1, 2), (2, –3), (4, 0)

and

(1, –3), (–1, 2), (–2, 3), (–4, 0)

4. (4, 1), (1, 2), (4, 5), (1, 5)

and

(–4, –1), (–1, –2), (–4, –5), (–1, –5)

none

rotation

Lesson Quiz: Part II