Concept Byte: Tracing Paper Transformations

Use With Lesson 9-3

ACTIVITY

In Lesson 9-1, you learned how to describe a translation using variables. In these activities, you will use tracing paper to perform translations, rotations, and reflections. You will also describe certain rotations and reflections using variables.

Activity 1

You can use the vector arrow shown in the diagram to represent the translation ( x , y ) → ( x + 4 , y + 2 ) . open x comma y close rightwards arrow . open x plus 4 comma y plus 2 close .  The translation shifts Δ A B C cap delta eh b c  with A ( − 3 , 3 ) , B ( − 1 , 1 ) , and  C ( 1 , 4 ) eh open negative 3 comma 3 close comma b open negative 1 comma 1 close comma , and c open 1 comma 4 close  to Δ A ′ B ′ C ′ cap delta , eh prime , b prime , c prime  with A ′ ( 1 , 5 ) , B ′ ( 3 , 3 ) and  C ′ ( 5 , 6 ) . eh prime , open 1 comma 5 close comma , b prime , open 3 comma 3 close , and , c prime , open 5 comma 6 close .  You can see this translation using tracing paper as follows:

• Step 1 Draw Δ A B C cap delta eh b c  and the vector arrow on graph paper. Also, show the line containing the arrow.
• Step 2 Trace Δ A B C cap delta eh b c  and the vector arrow.
• Step 3 Move your tracing of the vector arrow along the vector line until the tail of the tracing is on the head of the original vector arrow. The vertices of your tracing of Δ A B C cap delta eh b c  should now be at A ′ ( 1 , 5 ) , B ′ ( 3 , 3 ) , and  C ′ ( 5 , 6 ) . eh prime , open 1 comma 5 close comma , b prime , open 3 comma 3 close comma , and , c prime , open 5 comma 6 close .

  

Use tracing paper. Find the translation image of each triangle for the given vector.

1. 
2. 
3. 
4. Show that the composition of the translation in Question 1 followed by the translation in Question 2 gives you the translation in Question 3.

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