Question

LESSON 3 WORK WITH SEQUENCES OF TRANSFORMATIONS AND CONGRUENCE

Activity Thinking About Sequences
Have you ever rearranged furniture in a room? When you
move a chair from one side of the room to another, this can
How many ways can you describe the movement of
the furniture between the before and after pictures?
LESS
Before
Ex
Tri
of Transformations Around You
> Do this activity together to describe sequences of
transformations in the real world.
Pre
tra
yo
be described as a sequence of transformations!
?
After

Answer 1

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Answer:

an infinite number of ways

Explanation:

The transformation involves a series of reflections, rotations, and translations. Any reflection and translation can be described an infinite number of ways, depending on what you choose for the line of reflection (and how many reflections you choose), and how far you do each translation. Similarly, any rotation can described an infinite number of ways, depending on the amount of rotation and the chosen center point.

So, the answer to the question asked is, "You can describe the movement of the furniture an infinite number of ways."

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One way to describe it is this:

The upper chair was translated to the right, then reflected* across the horizontal centerline. The couch was rotated 90° about the center of the room and translated upward. The coffee table was rotated -90° about its center and translated to the right.

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* As a practical matter, a piece of furniture cannot be reflected. It can only be rotated or translated. However, the pillows in the upper chair are moved from the left arm to the right arm, so the appearance is that of a reflection. One might say the chair was rotated 180°, and the pillows were translated.