Holt CA Course 1

8-7 Transformations

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California StandardsCalifornia Standards

Lesson Presentation

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Holt CA Course 1

8-7 Transformations

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(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).

Holt CA Course 1

8-7 Transformations

MG3.2 Understand and use coordinate graphs to plot simple figures, determine lengths and areas related to them, and determine their image under translations and reflections.

California

Standards

Holt CA Course 1

8-7 Transformations

Vocabulary

transformationimagetranslationreflectionrotation

Holt CA Course 1

8-7 Transformations

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

Holt CA Course 1

8-7 Transformations

Holt CA Course 1

8-7 Transformations

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.

Holt CA Course 1

8-7 Transformations

The point that a figure rotates around may be on the figure or away from the figure.

Helpful Hint

Holt CA Course 1

8-7 TransformationsCheck It Out! Example 1

Identify each type of transformation.

A. B.

x

y

2

2

–2

–4

4

4

–4

–2 0

x

y

2

2

–2

–4

4

4

–4

–2 0

It is a translation.

The figure slides along a straight line.

It is a rotation.

The figure turns around a fixed point.

Holt CA Course 1

8-7 TransformationsAdditional 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.

Holt CA Course 1

8-7 Transformations

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

Holt CA Course 1

8-7 Transformations

Check It Out! Example 2

Translate quadrilateral ABCD 5 units left and 3 units down.

Each vertex is moved five units left and three units down.

x

yA

B

C

2

2

–2

–4

4

4

–4

–2 D

D’C’

B’A’

Holt CA Course 1

8-7 Transformations

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

A. x-axis

Additional Example 3: Graphing Reflections on a Coordinate Plane

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), C’(2, –2).

Holt CA Course 1

8-7 Transformations

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), C’(–2, 2).

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

Holt CA Course 1

8-7 TransformationsCheck It Out! Example 3

3

x

y

A

B

C

3

–3

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’B’C are A’(1, 0), B’(3, –3), C’(5, 0).

A’

B’

C’

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

A. x-axis

Holt CA Course 1

8-7 TransformationsCheck It Out! Example 3

A x

y

B

C

3

3

–3

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’B’C are A’(0, 0), B’(–2, 3), C’(–2, –3).C’

B’

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

B. y-axis

Holt CA Course 1

8-7 Transformations

Triangle ABC has vertices A(1, 0), B(3, 3), C(5, 0). Rotate ∆ABC 180° about the vertex A.

Additional Example 4: Graphing Rotations on a Coordinate Plane

x

y

A

B

C

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’

–3

Holt CA Course 1

8-7 Transformations

Triangle ABC has vertices A(–2, 0), B(0, 3), C(0, –3). Rotate ∆ABC 180° about the vertex A.

Check It Out! Example 4

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

Notice that vertex B is 2 units to the right and 3 units above vertex A, and vertex B’ is 2 units to the left and 3 units below vertex A.

x

y

B

C

4

3

–4B’

C’

A

Holt CA Course 1

8-7 Transformations

Lesson Quiz: Part I

1. Identify the transformation.

(1, –4), (5, –4), (9, 4)

reflection

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

Holt CA Course 1

8-7 TransformationsLesson Quiz: Part II

3. Graph the triangle with vertices A(–1, 0), B(–3, 0), C(–1, 4). Rotate ∆ABC 90° counterclockwise around vertex B and reflect the resulting image across the y-axis.