QuizDetermine the slope of each line.

1. PQ

2. MN

3. Which pair of lines are parallel?

In the figure, WXYZ ABCD

4. Find XY.

5. Find mB.

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

Warm Up

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

transformation

translation

rotation

center of rotation

reflection

image

Vocabulary

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.

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

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

A. B.

reflection rotation

Example: Identifying Transformations

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

C. D.

none of the these translation

Example: Identifying Transformations

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’

Try This

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

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’

Example: Drawing Transformations

Draw the image of the triangle after the transformation.

A

B

C

B. Reflection across BC.

A’

B’

C’

Example: Drawing Transformations

Draw the image of the triangle after the transformation.

A

B

C

C. 90° clockwise rotation around point B A’

B’

C’

Example: Drawing Transformations

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

Try This

Draw the image of the polygon after the transformation.

A

BC

D

E

F

B. Reflection across CD.

A’

B’C’

D’

E’

F’

Try This

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

Reflection and Translation

Dilation and Rotation

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)

Example: 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

Example: 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

Example: Graphing Transformations

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

Try This

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.

x

y

–2

2

Try This

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.

x

y

–2

2

Try This

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

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.

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