Section 12-1 Transformations - Reflection SPI 32D: determine whether the plane figure has been reflected given a diagram and vice versa

1
Section 12-1 Transformations -
Reflection SPI 32D
determine whether the plane figure has been
reflected given a diagram and vice versa

• Objectives
• Identify isometries
• Find reflection images of figures

Unit Overview

• Investigate Transformations
• Reflections (this lesson)
• Translations
• Rotations
• Composition of Transformations

2
Vocabulary
Transformation is a change in the original figure
(preimage)
Shape
Size
Position
Preimage
3
Some Basic Transformations
Figure Flips
Figure Slides
Preimage
Image
Preimage
Image
Figure Turns
Image
Preimage
4
Identifying Isometries
Isometry
Transformation in which the preimage and image
are ?.
Isometry
NOT Isometry (not congruent)
5
Transformation Symbols and Notation
Transformation maps a figure onto its image.

• mapping is shown with an arrow. (?)

• corresponding image points are shown with a
  prime symbol ()

Write transformation as
preimage
image
6
DO Now
Naming Images and
Corresponding Parts
In the diagram, XYZ is an image of ABC.
a. Name the images of B and C.
b. List all pairs of corresponding sides.
?Y is the image of?B
AB and XY, BC and YZ, AC and XZ
?Z is the image of?C
7
Finding Reflection (Flip) Images
Isometry in which figure and its image have
opposite orientation.
Reflection
a
Line a is the line of reflection
Written as ?BUG ? ?BUG
8
Finding Reflection (Flip) Images
In geometric terms, a reflection in line r is a
transformation for which the following are true

• If a point A is on line r, then the image of A
  is A itself

• If a point B is not on line r, then r is the ?
  bisector of BB

9
Relate Reflections to the Coordinate Plane
?XYZ has vertices X(0, 3), Y(2, 0), and Z(4, 2).
Draw ? XYZ and its reflection image in the line x
4.
10
Real-World Using Reflection to install
Security Camera
Suppose you are hired by a
security company to install a security camera.
The camera is located as shown in the diagram.
At what point on the mirrored wall should you aim
the camera in order to videotape the door D?
D
What is the line of reflection?
Reflections
Mirrored wall
Reflect D over the mirrored wall.
Connect C and D.
The camera should be focused on the intersection
of the segment wall.