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Lesson 4Making the Moves

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

Learning Targets:

  • 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.

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4.2 Make That Move

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

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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.)

  1. Name a transformation that takes Figure A to Figure B. Name a transformation that takes Figure B to Figure C.

  2. What is one sequence of transformations that takes Figure A to Figure C? Explain how you know.

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Translate

  1. Select the Vector tool.
  2. Click on the original point and then the new point; you should see a vector. 
  3. Select the Translate by Vector tool. 
  4. Click on the figure to translate, and then click on the vector.

Rotate

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

Reflect

  1. Select the Reflect about Line tool. 
  2. 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 A to Figure C . 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  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 ABCD 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 ABCDEF 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 ABCDE 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.

Glossary Terms

sequence of transformations

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 \ell to make C.

Figure A is transformed to become Figure B and then Figure C.
transformation

A transformation is a translation, rotation, reflection, or dilation, or a combination of these.

Lesson 4 Practice Problems

  1. For each pair of polygons, describe a sequence of translations, rotations, and reflections that takes Polygon P to Polygon Q.

    1. two of the same figure on an isometric grid in different orientations and position
    2. two of the same figure on an isometric grid in different orientations and position
    3. two of the same figure in different orientations and position.

  2. Here is quadrilateral ABCD and line \ell .

    Quadrilateral ABCD is shown next to line l

    Draw the image of quadrilateral ABCD after reflecting it across line \ell .

  3. Here is quadrilateral ABCD .

    Quadrilateral ABCD is shown

    Draw the image of quadrilateral ABCD after each rotation using B as center.

    1. 90 degrees clockwise
    2. 120 degrees clockwise
    3. 30 degrees counterclockwise