Sect. 7.1 Rigid Motion in a Plane

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Presentation transcript:

Sect. 7.1 Rigid Motion in a Plane Goal 1 Identify the three basic rigid transformations Goal 2 Use transformations in real-life situations.

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.

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

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?

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.

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.

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

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

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?

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

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

Using Transformations in Real Life

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 )

Homework 7.1 6 - 28 even, 36-39