Lesson 4Making the Moves

Learning Goal

Let’s draw and describe translations, rotations, and reflections.

Learning Targets

I can use the terms translation, rotation, and reflection to precisely describe transformations.

Lesson Terms

clockwise
counterclockwise
image
reflection
rotation
sequence of transformations
transformation
translation
vertex

Warm Up: Reflection Quick Image

Here is an incomplete transformation. Your teacher will display the completed transformation twice, for a few seconds each time. Your job is to complete the transformation on your copy.

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Here is an incomplete transformation. Your teacher will display the completed transformation twice, for a few seconds each time. Your job is to complete the transformation on your copy.

A right triangle A, B, C on a square grid. The right angle is at B.

Activity 1: Make That Move

Your partner will describe the image of this triangle after a certain transformation. Sketch it here.

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Your partner will describe the image of this triangle after a certain transformation. Sketch it here.

Activity 2: A to B to C

Here are some figures on an isometric grid. Explore the transformation tools in the tool bar. (Directions are below the applet if you need them.)

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Translate

Select the Vector tool.
Click on the original point and then the new point. You should see a vector.
Select the Translate by Vector tool.
Click on the figure to translate, and then click on the vector.

Rotate

Select the Rotate around Point tool.
Click on the figure to rotate, and then click on the center point.
A dialog box will open. Type the angle by which to rotate and select the direction of rotation.

Reflect

Select the Reflect about Line tool.
Click on the figure to reflect, and then click on the line of reflection.

Name a transformation that takes Figure $A$ to Figure $B$ . Name a transformation that takes Figure $B$ to Figure $C$ .
What is one sequence of transformations that takes Figure $A$ to Figure $C$ ? Explain how you know.

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Here are some figures on an isometric grid.

Three trapezoid, blue A, green B and green C, on an isometric grid.

Name a transformation that takes Figure $A$ to Figure $B$ . Name a transformation that takes Figure $B$ to Figure $C$ .
What is one sequence of transformations that takes Figure $A$ to Figure $C$ ? Explain how you know.

Are you ready for more?

Experiment with some other ways to take Figure $A$ to Figure $C$ . For example, can you do it with …

No rotations?
No reflections?
No translations?

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Experiment with some other ways to take Figure $A$ to Figure $C$ . For example, can you do it with …

No rotations?
No reflections?
No translations?

Lesson Summary

A move, or combination of moves, is called a transformation. When we do one or more moves in a row, we often call that a sequence of transformations. To distinguish the original figure from its image, points in the image are sometimes labeled with the same letters as the original figure, but with the symbol $^{'}$ attached, as in $A^{'}$ (pronounced “A prime”).

A translation can be described by two points. If a translation moves point $A$ to point $A^{'}$ , it moves the entire figure the same distance and direction as the distance and direction from $A$ to $A^{'}$ . The distance and direction of a translation can be shown by an arrow.

For example, here is a translation of quadrilateral $A B C D$ that moves $A$ to $A^{'}$ .

A quadrilateral A, B, C, D, and its translation to A prime, B prime, C prime, D prime.

A rotation can be described by an angle and a center. The direction of the angle can be clockwise or counterclockwise.

For example, hexagon $A B C D E F$ is rotated $90^{\circ}$ counterclockwise using center $P$ .

A hexagon A, B, C, D, E, F, and its rotation 90 degrees bout a center, P, to hexagon A prime, B prime, C prime, D prime, E prime, F prime.

A reflection can be described by a line of reflection (the “mirror”). Each point is reflected directly across the line so that it is just as far from the mirror line, but is on the opposite side.

For example, pentagon $A B C D E$ is reflected across line $m$ .

A pentagon A, B, C, D, E, and its reflection in a line m, to pentagon A prime, B prime, C prime, D prime, E prime.

Lesson 4Making the Moves

Learning Goal

Learning Targets

Lesson Terms

Warm Up: Reflection Quick Image

Problem 1

Activity 1: Make That Move

Problem 1

Activity 2: A to B to C

Problem 1

Are you ready for more?

Problem 1

Lesson Summary