learn to recognize, describe, and show transformations. course 2 8-10 translations, reflections, and...

Learn to recognize, describe, and show transformations.

Course 2

8-10 Translations, Reflections, and Rotations

Vocabulary

transformationimagetranslationreflectionline of reflectionrotation

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Course 2


A translation "slides" an object a fixed distancein a given direction. The original object and its translation have

the same shape and size, and they face in the same direction. The word "translate" in Latin means "carried across".

Think of polygon ABCDE as sliding two inches to the right and one inch down. Its new

position is labeled A'B'C'D'E'.

A translation moves an

objectwithout changing its size

or shape and without turning it or flipping it.

Remember:

Translations are SLIDES!!! Translations are SLIDES!!!

A reflection can be seen in water, in a mirror, in glass, or in a shiny surface. An object and its reflection have the same

shape and size, but the figures face in opposite directions. In a mirror, for example, right and left are

switched.

The line (where a mirror may be placed) is called the line of reflection. The distance from a point to the line of reflection is the same as the distance from the point's image to the line of reflection. A reflection can be thought of as a "flipping" of an object over the line of reflection.

Remember:Reflections are FLIPS!!!

A rotation is a transformation that turns a figure about a fixed point called the center of rotation. An object and its rotation

are the same shape and size, but the figures may be turned in different directions.

Remember:

Rotations are TURNS!!!

This rotation is 90 degrees counterclockwise.

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.Course 2


It is a reflection.

The figure slides along a straight line.


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

Helpful Hint

Check It Out: Example 1

Identify each type of transformation.

A. B.


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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.

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.

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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

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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’

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

x-axis, then y-axis

Additional Example 3: Graphing Reflections on a Coordinate Plane

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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.

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

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.

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

Check It Out: Example 3A


3

x

y

A

B

C

3

–3

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Graph the reflection of the triangle ABC across the x-axis. Write the coordinates of the vertices of the image.

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

A’

B’

C’

Check It Out: Example 3B


A x

y

B

C

3

3

–3

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Graph the reflection of the triangle ABC across the y-axis. Write the coordinates of the vertices of the image.

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

B’

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

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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’

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


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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

3

3

–3B’

C’

A

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?

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Lesson 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.


Course 2


x

y

2

–2

2–2–4

–4

4

4

C

B AC’

B’

A’

C’’A’’

B’’

learn to recognize, describe, and show transformations. course 2 8-10 translations, reflections, and...

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