8-5 translations, reflections, and rotations in mathematics, a transformation changes the position...

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.


TranslationThe figure slides along a straight line without turning.

Types of Transformations


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



RotationThe figure turns around a fixed point.



Identify each type of transformation.

Additional Example 1: Identifying Types of Transformations

The figure flips across the y-axis.

A. B.

The figure slides along a straight line.


Check It Out: Example 1

Identify the type of transformation.


Additional Example 2: Graphing Transformations on a Coordinate Plane

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


Write the coordinate of the vertices of the image.

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

A(1, 3)

B(4, 4)

C(4, 1)

D(1, –1)


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



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

x

y

AB

C

2

2

–2

4

4

–4

D


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


A. x-axis

Additional Example 3 Continued

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


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



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

x

y

AB

C

2

2

–2

4

4

–4

D


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’


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


x

y

AB

C

2

2

–2

4

4

–4

D


Lesson Quiz

1. Identify the transformation.


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.


1. Identify the transformation.

A. translation

B. reflection

C. rotation

D. none

Lesson Quiz for Student Response Systems


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

8-5 translations, reflections, and rotations in mathematics, a transformation changes the position...

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