Math 8 Unit 1 Lesson 4: Making the Moves

Author:Lindsay Rice, IM 6 – 8 Math, GeoGebra Classroom Activities

Adapted from Open Up Resources https://openupresources.org/

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

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

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 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 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 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 counterclockwise using center P.

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.

Lesson 4 Cool Down: What Does it Take?

If you were to describe a translation of triangle ABC, what information would you need to include in your description?

If you were to describe a rotation of triangle ABC, what information would you need to include in your description?

If you were to describe a reflection of triangle ABC, what information would you need to include in your description?