8-5 Translations, Reflections, and Rotations

Warm UpWarm Up

Lesson PresentationLesson Presentation

Problem of the DayProblem of the Day

Lesson QuizzesLesson Quizzes

8-5 Translations, Reflections, and Rotations

Warm Up

(4, –6)

(12, 27)

(–6, 2)

1. Subtract 3 from the x-coordinate and 2 from the y-coordinate in (7, –4).

2. Multiply each coordinate by 3 in (4, 9).

3. Subtract 4 from the x-coordinate and add 3 to the to the y-coordinate in (–2, –1).

8-5 Translations, Reflections, and Rotations

Problem of the Day

Some numbers appear as different numbers when rotated or reflected. Name as many as you can.

Possible answers: 6 and 9; 6999 and 6669; IV and VI; IX and XI

8-5 Translations, Reflections, and Rotations

MA.7.G.4.2 Predict the results of transformations and draw transformed figures, with and without the coordinate plane.Also MA.7.G.4.3

Sunshine State Standards

8-5 Translations, Reflections, and Rotations

Vocabulary

transformationimagepreimagetranslationreflectionline of reflectionrotation

8-5 Translations, Reflections, and Rotations

In mathematics, a transformationchanges the position or orientation of a figure. The resulting figure is the imageof the original figure, called the preimage. Images resulting from the transformations described in the next slides are congruent to the original figures.

8-5 Translations, Reflections, and Rotations

TranslationThe figure slides along a straight line without turning.

Types of Transformations

8-5 Translations, Reflections, and Rotations

ReflectionThe figure flips across a line of reflection, creating a mirror image.

Types of Transformations

8-5 Translations, Reflections, and Rotations

RotationThe figure turns around a fixed point.

Types of Transformations

8-5 Translations, Reflections, and Rotations

Identify each type of transformation.

Additional Example 1: Identifying Types of Transformations

The figure flips across the y-axis.

A. B.

It is a translation.It is a reflection.

The figure slides along a straight line.

8-5 Translations, Reflections, and Rotations

Check It Out: Example 1

Identify the type of transformation.

translation

8-5 Translations, Reflections, and Rotations

Additional Example 2: Graphing Transformations on a Coordinate Plane

Graph the translation of quadrilateral ABCD 4 units left and 2 units down.

Each vertex is moved 4 units left and 2 units down.

8-5 Translations, Reflections, and Rotations

Additional Example 2 Continued

Write the coordinate of the vertices of the image.

The coordinates of the vertices of quadrilateral A'B'C'D' are A'(–3, 1), B'(0, 2), C'(0, –1), and D'(–3, –3).

Quadrilateral ABCD (x – 4, y – 2) A’B’C’D’

A(1, 3) (1 – 4, 3 – 2) A’(–3, 1)

B(4, 4) (4 – 4, 4 – 2) B’(0, 2)

C(4, 1) (4 – 4, 1 – 2) C’(0, –1)

D(1, –1) (1 – 4, –1 – 2) D’(–3, –3)

8-5 Translations, Reflections, and Rotations

A’ is read “A prime” and is used to represent the point on the image that corresponds to point A of the original figure

Reading Math

8-5 Translations, Reflections, and Rotations

Check It Out: Example 2

Graph the translation of quadrilateral ABCD 5 units left and 3 units down.

x

yA

B

C

2

2

–2

–4

4

4

–4

–2 D

D’C’

B’A’

8-5 Translations, Reflections, and Rotations

Graph the reflection of the figure across the indicated axis. Write the coordinates of the vertices of the image.

Additional Example 3: Graphing Reflections on a Coordinate Plane

8-5 Translations, Reflections, and Rotations

A. x-axis

Additional Example 3 Continued

The x-coordinates of the corresponding vertices are the same, and the y-coordinates of the corresponding vertices are opposites.

The coordinates of the vertices of triangle A’D’C’ are A’(–3, –1), D’(0, 0), and C’(2, –2).

8-5 Translations, Reflections, and Rotations

B. y-axis

Additional Example 3 Continued

The y-coordinates of the corresponding vertices are the same, and the x-coordinates of the corresponding vertices are opposites.

The coordinates of the vertices of triangle A’D’C’ are A’(3, 1), D’(0, 0), and C’(–2, 2).

8-5 Translations, Reflections, and Rotations

Check It Out: Example 3

Graph the reflection of quadrilateral ABCD across the x-axis.

8-5 Translations, Reflections, and Rotations

Triangle ABC has vertices A(1, 0), B(3, 3), C(5, 0). Rotate ∆ABC 180° about the origin. Write the coordinates of the vertices of the image.

Additional Example 4: Graphing Rotations on a Coordinate Plane

x

y

A

B

C

3

–3

The corresponding sides, AC and AC’ make a 180° angle.

Notice that vertex C is 4 units to the right of vertex A, and vertex C’ is 4 units to the left of vertex A.

C’

B’

A’

The coordinates of the vertices of triangle A’B’C’ are A’(0, 0), B’(–2, –3), and C’(–4, 0).

8-5 Translations, Reflections, and Rotations

Rotate the graph of quadrilateral ABCD 90° clockwise about the origin.

Check It Out: Example 4

8-5 Translations, Reflections, and Rotations

Standard Lesson Quiz

Lesson Quizzes

Lesson Quiz for Student Response Systems

8-5 Translations, Reflections, and Rotations

Lesson Quiz

1. Identify the transformation.

(1, –4), (5, –4), (9, 4)

reflection

2. The figure formed by (–5, –6), (–1, –6), and(3, 2) is translated 6 units right and 2 units up. What are the coordinates of the new figure?

3. Graph the triangle with vertices A(0, 0), B(–3, 0), C(–1, 4). Reflect ∆ABC across the y-axis and give the coordinates of the vertices of the image.

A'(0, 0), B'(3, 0), C'(1, 4)

8-5 Translations, Reflections, and Rotations

1. Identify the transformation.

A. translation

B. reflection

C. rotation

D. none

Lesson Quiz for Student Response Systems

8-5 Translations, Reflections, and Rotations

2. The figure formed by (–3, 2), (–4, 1), and (–1, –5) is translated 3 units right and 5 units up. What are the coordinates of the new figure?

A. (–6, –3), (–7, –4), (–4, –10)

B. (0, 7), (–7, –4), (2, –10)

C. (0, 7), (–1, 6), (2, 0)

D. (–6, –3), (–1, 6), (–4, 0)

Lesson Quiz for Student Response Systems