Lesson 2Naming the Moves

Learning Goal

Let’s be more precise about describing moves of figures in the plane.

Learning Targets

  • I can identify corresponding points before and after a transformation.

  • I know the difference between translations, rotations, and reflections.

Lesson Terms

  • clockwise
  • corresponding
  • counterclockwise
  • image
  • reflection
  • rotation
  • translation
  • vertex

Warm Up: A Pair of Quadrilaterals

Problem 1

Quadrilateral can be rotated into the position of Quadrilateral .

Estimate the angle of rotation.

Two identical quadrilaterals labeled A and B that meet at a point.

Activity 1: How Did You Make That Move?

Here is another set of dance moves.

6 panels showing the same figure in different positions and orientations.

Problem 1

Describe each move or say if it is a new move.

  1. Frame 1 to Frame 2.

  2. Frame 2 to Frame 3.

  3. Frame 3 to Frame 4.

  4. Frame 4 to Frame 5.

  5. Frame 5 to Frame 6.

Problem 2

How would you describe the new move?

Activity 2: Card Sort: Move

Problem 1

Your teacher will give you a set of cards. Sort the cards into categories according to the type of move they show. Be prepared to describe each category and why it is different from the others. You can explore the applets below to see the ways the images move.

Drag the red point. Explore how the image changes.

open applet in presentation mode
open applet in presentation mode

Click on the box to show the transformed image.

Move the yellow points and the red segment to see how the image changes.

open applet in presentation mode
Print Version

Your teacher will give you a set of cards. Sort the cards into categories according to the type of move they show. Be prepared to describe each category and why it is different from the others.

Lesson Summary

Here are the moves we have learned about so far:

A translation slides a figure without turning it. Every point in the figure goes the same distance in the same direction. For example, Figure A was translated down and to the left, as shown by the arrows. Figure B is a translation of Figure A.

Two figures, one labelled A, and its translation, labelled B.

A rotation turns a figure about a point, called the center of the rotation. Every point on the figure goes in a circle around the center and makes the same angle. The rotation can be clockwise, going in the same direction as the hands of a clock, or counterclockwise, going in the other direction. For example, Figure A was rotated clockwise around its bottom vertex. Figure C is a rotation of Figure A.

Two figures, one labelled A, and its rotation, labelled C.

A reflection places points on the opposite side of a reflection line. The mirror image is a backwards copy of the original figure. The reflection line shows where the mirror should stand. For example, Figure A was reflected across the dotted line. Figure D is a reflection of Figure A.

Two figures, one labelled A, and its reflection, labelled D

We use the word image to describe the new figure created by moving the original figure. If one point on the original figure moves to another point on the new figure, we call them corresponding points.