1. Sect. 7.1 Rigid Motion in a Plane
Goal Identify the three basic rigid transformations
Goal Use transformations in real-life situations.

2. Identifying Transformations
Transformation – An operation that maps, or moves, one figure onto another. The original figure is called the preimage and the new figure is called the image.

3. Translations Reflections Rotations
Transformations
Operation that maps, or moves, a figure (preimage) onto a new figure (image).
Translations
Reflections
Rotations

4. Use the graph of the transformation.
EXAMPLE 1
Naming Transformations
Use the graph of the transformation.
Name and describe the transformation.
Name the coordinates of the vertices of the image.
Is ABC congruent to its image?

5. Use the graph of the transformation below.
EXAMPLE 1
Naming Transformations - Practice
Use the graph of the transformation below.
Name and describe the transformation.
Name the coordinates of the vertices of the image.
Name two angles with the same measure.

6. Isometry – transformation that preserves lengths.
Identifying Transformations
Isometry – transformation that preserves lengths.
Isometries also preserve angle measures, parallel lines, and distances between points.
Translations, rotations and reflections are all isometries.

7. Which of the following transformations appear to be isometries?
EXAMPLE 2
Identifying Isometries
Which of the following transformations appear to be isometries?

8. Identifying Isometries - Practice
EXAMPLE 2
Identifying Isometries - Practice
State whether the transformation appears to be an isometry.

9. EXAMPLE 3
Preserving Length and Angle Measure
PQR is mapped onto XYZ. The mapping is a rotation. Given that PQR  XYZ is an isometry, find the length of and the mZ?

10. Preserving Length and Angle Measure - Practice
EXAMPLE 3
Find the value of each variable, given that the transformation is an isometry.

11. Preserving Length and Angle Measure - Practice
EXAMPLE 3
Find the value of each variable, given that the transformation is an isometry.

12. Using Transformations in Real Life

13. Challenge: Skills and Applications
Sketch the image of the given triangle after the given transformation. Given the coordinates of the image.
(x, y)  (x + 4 , y – 3)
(x, y)  (y, – x )

14. Homework
even, 36-39