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.

Print Version

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

Problem 1

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

Print Version

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

Blue triangle ABC on a grid.

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

  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.

  1. Name a transformation that takes Figure to Figure . Name a transformation that takes Figure to Figure .

  2. 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.

Three trapezoid, blue A, green B and green C, on an isometric grid.
  1. Name a transformation that takes Figure to Figure . Name a transformation that takes Figure to Figure .

  2. 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 to Figure . For example, can you do it with …

  • No rotations?

  • No reflections?

  • No translations?

Print Version

Experiment with some other ways to take Figure to Figure . 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 (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 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 is rotated counterclockwise using center .

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 is reflected across line .

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.