Rigid Motions

Rigid Transformations​

​An Introduction

TL;DR

In this lesson, we are going to learn how to move a figure from one place to another on grid paper, using precise mathematical rules.

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There are three basic 'moves' we can make to get a figure from one place to another. Check out the next slide to see what those are.

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No matter how we do it, moving a figure does not change its size or shape.​

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These moves are called Rigid Transformations.​

Subject | Subject

Some text here about the topic of discussion

A Rigid Transformation is a set of motions that moves one figure on a plane onto another figure.

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Rigid Transformations Preserve Congruence.​

What are they?​

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We will practice working with three rigid transformations:

1. Translations.

2. Reflections.

3. Rotations.​

Types of Rigid Transformations

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When moving a figure across the page, we don't change its size or shape, the original figure is Congruent to the new figure.

What are they?​

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We will practice working with three rigid transformations:

1. Translations.

2. Reflections.

3. Rotations.​

Types of Rigid Transformations

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When moving a figure across the page, we don't change its size or shape, the original figure is Congruent to the new figure.

What are they?​

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The original figure is called the pre image.

The result from moving a figure is called the image.​

​Notice how the points change (and how they don't)​.

​Write this down!

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Multiple Select

Which of the following are Rigid Transformations?

• Reflection

• Translation

• Contemplation

• Rotation

Multiple Choice

What do we call the original figure after performing a rigid transformation?

• Pre Image

• Image

Multiple Choice

What do we call the figure after performing a rigid transformation?

• Pre Image

• Image

Multiple Choice

We say that rigid transformations dont change the size or shape of a figure. What does this mean?

• What does anything mean really? We're just a blip in the universe; a sound that can't be heard, a face that can't be seen - destined to be forgotten before we're realized. (-//-)

• The figures are not congruent.

• The figures are congruent

We call these slides because thats basically what you do, you slide an object in one direction.

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How far, and in what direction?

Using​ a directed line segment, we can tell what direction and how far to go by measuring the distance of that line segment.

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Notice DE at the top? That is our guide, a directed line segment. ​

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​just a blip in the universe...

​Translations

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​just a blip in the universe...

Also the equal sign with toothpaste on top is the symbol for Congruence. Write that down. ​

Sorry for the tiny squares...​

​Translations

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When every point of a figure ends up on the other side of a line, we call this a reflection.​ It's not that simple, there are some rules to consider:

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Every set of points must be equidistant from the line.​

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​You have to reflect over something, we call this the line of reflection.

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You go in the direction perpendicular to the line.​

Equidistant means that they have the same length. From point A to the line is the same length as point A' to the line.

Perpendicular means at a right angle.​

Reflections

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When every point of a figure ends up on the other side of a line, we call this a reflection.​ It's not that simple, there are some rules to consider:

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Every set of points must be equidistant from the line.​

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​You have to reflect over something, we call this the line of reflection.

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You go in the direction perpendicular to the line.​

Equidistant means that they have the same length. From point A to the line is the same length as point A' to the line.

Perpendicular means at a right angle.​

Reflections

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​Every point of the figure moves in a circle around some other point called the center of rotation.

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​Rotations can happen clockwise or counterclockwise around the center.

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When performing a rotation, there should be an angle ​of rotation that tells us how far to go.

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In the image to your right, the center is point D.​

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​Clockwise goes to the right like the hands on a clock.

Counterclockwise goes left, not like the hands on a clock. .-. ​

RotatioNs​

Each point is rotated by the same amount, using the same angle.

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​Take a look at point C!

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​Clockwise goes to the right like the hands on a clock.

Counterclockwise goes left, not like the hands on a clock. .-. ​

Rotations​

Each point is rotated by the same amount, using the same angle.

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​It's hard to tell here, but every point is being rotated by 45 degrees clockwise.

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​Clockwise goes to the right like the hands on a clock.

Counterclockwise goes left, not like the hands on a clock. .-. ​

Rotations​

Each point is rotated by the same amount, using the same angle.

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​It's hard to tell here, but every point is being rotated by 45 degrees clockwise.

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We will use triangular grid paper in class to measure the angle of rotation a bit easier with our compass.

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​Clockwise goes to the right like the hands on a clock.

Counterclockwise goes left, not like the hands on a clock. .-. ​

Rotations​

Each point is rotated by the same amount, using the same angle.

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​It's hard to tell here, but every point is being rotated by 45 degrees clockwise.

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We will use triangular grid paper in class to measure the angle of rotation a bit easier with our compass.

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​The compass will make plotting points a lot easier as well.

​Clockwise goes to the right like the hands on a clock.

Counterclockwise goes left, not like the hands on a clock. .-. ​

Rotations​

Multiple Choice

What kind of transformation is this?

• Rotation

• Reflection

• Translation

Multiple Choice

What kind of transformation is this?

• Rotation

• Reflection

• Translation

Multiple Choice

What kind of transformation is this?

• Rotation

• Reflection

• Translation

Fill in the Blank

Rigid transformations preserve ....

Multiple Choice

What is another way to describe a translation?

• Teleport

• Jump

• Glide

• Slide

Multiple Choice

When reflecting a figure, you reflect across

• the page

• The line of reflection

• The center point

Multiple Select

What is needed when performing a rotation?

• A center of rotation

• An angle of rotation

• A calculator

• A compass to measure the angle of rotation and position of the points.

Multiple Select

What is needed when performing a reflection?

• A center of rotation

• All sets of points to be equidistant from the line of reflection

• A line of reflection

• The direction to be perpendicular to the line of reflection.