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
Problem 1
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.
Activity 1: Make That Move
Problem 1
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
Problem 1
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.)
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
to Figure . Name a transformation that takes Figure to Figure . What is one sequence of transformations that takes Figure
to Figure ? Explain how you know.
Print Version
Here are some figures on an isometric grid.
Name a transformation that takes Figure
to Figure . Name a transformation that takes Figure to Figure . What is one sequence of transformations that takes Figure
to Figure ? Explain how you know.
Are you ready for more?
Problem 1
Experiment with some other ways to take Figure
No rotations?
No reflections?
No translations?
Print Version
Experiment with some other ways to take Figure
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
A translation can be described by two points. If a translation moves point
For example, here is a translation of quadrilateral
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 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