Lesson 4Making the Moves
Let’s draw and describe translations, rotations, and reflections.
- I can use the terms translation, rotation, and reflection to precisely describe transformations.
4.1 Reflection Quick Image
Here is an incomplete image. Your teacher will flash the completed image twice. Your job is to complete the image on your copy.
4.2 Make That Move
Your partner will describe the image of this triangle after a certain transformation. Sketch it here.
4.3 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.)
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.
- 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.
- 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.
- Select the Reflect about Line tool.
- Click on the figure to reflect, and then click on the line of reflection.
Are you ready for more?
Experiment with some other ways to take Figure to Figure . For example, can you do it with. . .
- No rotations?
- No reflections?
- No translations?
Lesson 4 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 (pronounced “A prime”).
A translation can be described by two points. If a translation moves point to point , it moves the entire figure the same distance and direction as the distance and direction from to . The distance and direction of a translation can be shown by an arrow.
For example, here is a translation of quadrilateral that moves to .
- A rotation can be described by an angle and a center. The direction of the angle can be clockwise or counterclockwise.
For example, hexagon is rotated counterclockwise using center .
- 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 is reflected across line .
A sequence of transformations is a set of translations, rotations, reflections, and dilations on a figure. The transformations are performed in a given order.
This diagram shows a sequence of transformations to move Figure A to Figure C.
First, A is translated to the right to make B. Next, B is reflected across line to make C.
A transformation is a translation, rotation, reflection, or dilation, or a combination of these.
Lesson 4 Practice Problems
For each pair of polygons, describe a sequence of translations, rotations, and reflections that takes Polygon P to Polygon Q.
Here is quadrilateral and line .
Draw the image of quadrilateral after reflecting it across line .
Here is quadrilateral .
Draw the image of quadrilateral after each rotation using as center.
- 90 degrees clockwise
- 120 degrees clockwise
- 30 degrees counterclockwise