Pre-Algebra

5-7 Transformations

5-7 Transformations

Pre-Algebra

Warm Up

Problem of the Day

Lesson Presentation

Pre-Algebra

5-7 Transformations

Warm Up

Pre-Algebra

5-7 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

Pre-Algebra

5-7 Transformations

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.)

Move the 9 to the first triangle.

Pre-Algebra

5-7 Transformations

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

Pre-Algebra

5-7 Transformations

transformation

translation

rotation

center of rotation

reflection

image

Vocabulary

Pre-Algebra

5-7 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.

Pre-Algebra

5-7 Transformations

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

Pre-Algebra

5-7 Transformations

Additional Example 1A & 1B: Identifying Transformations

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

A. B.

reflection rotation

Pre-Algebra

5-7 Transformations

Additional Example 1C & 1D: Identifying Transformations

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

C. D.

none of the these translation

Pre-Algebra

5-7 Transformations

Try This: Example 1A & 1B

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’

Pre-Algebra

5-7 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

Try This: Example 1C & 1D

Pre-Algebra

5-7 Transformations

Additional Example 2A: Drawing Transformations

Draw the image of the triangle after the transformation.

A

B

C

A. Translation along AB so that A’ coincides with B

A’

B’

C’

Pre-Algebra

5-7 Transformations

Additional Example 2B: Drawing Transformations

Draw the image of the triangle after the transformation.

A

B

C

B. Reflection across BC.

A’

B’

C’

Pre-Algebra

5-7 Transformations

Draw the image of the triangle after the transformation.

A

B

C

C. 90° clockwise rotation around point B A’

B’

C’

Additional Example 2C: Drawing Transformations

Pre-Algebra

5-7 Transformations

Try This: Example 2A

Draw the image of the polygon after the transformation.

A

B C

D

E

F

A’

B’ C’

D’

E’

F’

A. Translation along DE so that E’ coincides with D

Pre-Algebra

5-7 Transformations

Try This: Example 2B

Draw the image of the polygon after the transformation.

A

BC

D

E

F

B. Reflection across CD.

A’

B’C’

D’

E’

F’

Pre-Algebra

5-7 Transformations

Draw the image of the polygon after the transformation.

A

BC

D

E

F

C’

A’

B’

D’

E’F’

C. 90° counterclockwise rotation around point C

Try This: Example 2C

Pre-Algebra

5-7 Transformations

Additional Example 3A: Graphing Transformations

Draw the image of a triangle with vertices of (1, 1), (2, –2 ), and (5, 0) after each transformation.

A. 180° counterclockwise rotation around (0, 0)

Pre-Algebra

5-7 Transformations

Additional Example 3B: Graphing Transformations

Draw the image of a triangle with vertices of (1, 1), (2, –2 ), and (5, 0) after each transformation.

B. Translation 5 units left

Pre-Algebra

5-7 Transformations

Additional Example 3C: Graphing Transformations

Draw the image of a triangle with vertices of (1, 1), (2, –2 ), and (5, 0) after each transformation.

C. Reflection across the x-axis

Pre-Algebra

5-7 Transformations

Try This: Example 3A

Draw the image of a shape with vertices of (1, –2), (3, 2), (7, 3), and (6, –1) after each transformation.

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

x

y

–2

2

Pre-Algebra

5-7 Transformations

B. Translation 10 units left

Draw the image of a shape with vertices of (1, –2), (3, 2), (7, 3), and (6, –1) after each transformation.

Try This: Example 3B

x

y

–2

2

Pre-Algebra

5-7 Transformations

C. Reflection across the x-axis

Draw the image of a shape with vertices of (1, –2), (3, 2), (7, 3), and (6, –1) after each transformation.

Try This: Example 3C

x

y

–2

2

Pre-Algebra

5-7 Transformations

Lesson Quiz: Part 1

Given 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

Pre-Algebra

5-7 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 2