1.1.1: Moving in the Plane

Lesson

Let's describe ways figures can move in the plane.

Exercise \(\PageIndex{1}\): Which One Doesn't Belong: Diagrams

Which one doesn't belong?

Figure \(\PageIndex{1}\): Four figures labeled A, B, C, and D. each figure is composed of two rays and a point that is located at the endpoints of the two rays. In figure A the two rays point in opposite directions. In figure B, one ray extends downward and to the right and the other ray extends upward and to the right. the two rays appear to form a right angle. In figure C, one ray extends downward and slightly to the left and the other ray extends downward and slightly to the right. The two rays appear to form an acute angle. In figure D, one ray extends upward and to the left and the other ray extends directly downward. The two rays appear to form an obtuse angle.

Exercise \(\PageIndex{2}\): Triangle Square Dance

Your teacher will give you three pictures. Each shows a different set of dance moves.

1. Arrange the three pictures so you and your partner can both see them right way up. Choose who will start the game.
   1. The starting player mentally chooses A, B, or C and describes the dance to the other player.
   2. The other player identifies which dance is being talked about: A, B, or C.
2. After one round, trade roles. When you have described all three dances, come to an agreement on the words you use to describe the moves in each dance.
3. With your partner, write a description of the moves in each dance.

Dance A:

Dance B:

Dance C:

Are you ready for more?

We could think of each dance as a new dance by running it in reverse, starting in the 6th frame and working backwards to the first.

1. Pick a dance and describe in words one of these reversed dances.
2. How do the directions for running your dance in the forward direction and the reverse direction compare?

Summary

Here are two ways for changing the position of a figure in a plane without changing its shape or size:

• Sliding or shifting the figure without turning it. Shifting Figure A to the right and up puts it in the position of Figure B.

Figure \(\PageIndex{2}\)

• Turning or rotating the figure around a point. Figure A is rotated around the bottom vertex to create Figure C.

Figure \(\PageIndex{3}\)

Practice

Exercise \(\PageIndex{3}\)

The six frames show a shape's different positions.

Figure \(\PageIndex{4}\)

Describe how the shape moves to get from its position in each frame to the next.

Exercise \(\PageIndex{4}\)

These five frames show a shape's different positions.

Figure 5 shows figure 4 facing the opposite way and is still on the bottom right side.

Describe how the shape moves to get from its position in each frame to the next.

Exercise \(\PageIndex{5}\)

Diego started with this shape.

Figure \(\PageIndex{6}\)

Diego moves the shape down, turns it 90 degrees clockwise, then moves the shape to the right. Draw the location of the shape after each move.