7.1 Rigid Motion in a Plane - PowerPoint PPT Presentation

7 1 rigid motion in a plane
1 / 16

  • Uploaded on
  • Presentation posted in: General

7.1 Rigid Motion in a Plane. Images and Preimages. Figures in a plane can be changed to produce a new figure or image. In this unit, we will be investigating 3 different methods for making new figures (images) from old ones. Later in the course we will investigate a fourth method.

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

Download Presentation

7.1 Rigid Motion in a Plane

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript

7 1 rigid motion in a plane

7.1 Rigid Motion in a Plane

Images and preimages

Images and Preimages

Figures in a plane can be changed to produce a new figure or image. In this unit, we will be investigating 3 different methods for making new figures (images) from old ones. Later in the course we will investigate a fourth method.

The new figure is called the image. The original figure is called the preimage (the one that came before).

Transformations and isometry

Transformations and Isometry

The operation that maps or moves the preimage onto the image is called a transformation (change).

An isometry is a transformation that preserves length, it is considered a rigid transformation or motion. The new figure or image is congruent to the original figure or preimage.

One way to use notation

One Way to Use Notation

The image or new figure can be named with different letters.

A second way to use notation

A Second Way to Use Notation

Sometimes we use the same letter to represent the preimage and the image so that it is clear to the reader that they aren’t just totally different images, but that they have a relationship to one another. Namely the image was produced by the preimage. Of course the letters can’t be exactly the same, or we won’t know which is which, like using the same name for all of your children. (Which one is George?) Using this type of notation- if the preimage is A, then the image is A’, which is read “A prime”. (Like George and George Jr)

What are the 3 transformations

What are the 3 Transformations?

1. Translations are accomplished by sliding the figure across the plane. (Hint-the “sl” in translation can remind you of the “sl” in slide.)

2. Reflections are accomplished by flipping the figure across a line of reflection, often the x or y axis, in the plane. (Hint- the “fl” in reflections can remind you of the “fl” in flip.)

3. Rotations are accomplished by turning the figure about a point, often the origin, in the plane. (Hint-you probably already know that a rotation is a turn.)

Note: Keep in mind that these transformations are rigid. They do not change the size and shape of the figure, but merely relocate the figure in the plane and/or change its orientation.

Illustrations of the 3 transformations

Illustrations of the 3 Transformations

  • 1. Translations ( or slides): this moves the figure to a new location with no change to the looks of the figure.

  • 2. Reflections: these are like mirror images as seen across a line or a point.

  • 3. Rotations: this turns the figure clockwise or counter-clockwise but doesn’t change the figure.


More illustrations

More Illustrations

As you look at the image determine the type of translation.

Art work

Floor tiling





More images

More images

Art work

Stained Glass Window





More images1

More images

Art work






An example from word

An example from Word



Does the transformation appear to be an isometry.







More examples

More Examples

Name the type of transformation that maps the unshaded right triangle (preimage) onto the shaded right triangle (image).







More examples1


8. Rotation



11. (9,2)

12. See Sketch

More Examples

Complete each statement.

Last example

Last Example

Find the value of the variables given the transformation is an isometry


3a + 1 = 10

3a = 9

a = 3

b = 4

  • Login