12.3. Geometric Translations http://www.ck12.org
- Write the translation rule for the vector translation from #3.
Answers:
- Look at the movement fromTtoT′.Tis (-3, 3) andT′is (3, -1). The change inxis 6 units to the right and the
change inyis 4 units down. Therefore, the translation rule is(x,y)→(x+ 6 ,y− 4 ). - The graph is the vector
⇀
ST. From the initial pointSit moves down 5 units and to the right 2 units.- It would be helpful to graph 4 ABC. To translate 4 ABC, add each component of the vector to each point to find
4 A′B′C′.
A( 3 ,− 1 )+〈− 4 , 5 〉=A′(− 1 , 4 )
B( 7 ,− 5 )+〈− 4 , 5 〉=B′( 3 , 0 )
C(− 2 ,− 2 )+〈− 4 , 5 〉=C′(− 6 , 3 )
- To write〈− 4 , 5 〉as a translation rule, it would be(x,y)→(x− 4 ,y+ 5 ).
Explore More
- What is the difference between a vector and a ray?
Use the translation(x,y)→(x+ 5 ,y− 9 )for questions 2-8.
- What is the image ofA(− 6 , 3 )?
- What is the image ofB( 4 , 8 )?
- What is the preimage ofC′( 5 ,− 3 )?
- What is the image ofA′?
- What is the preimage ofD′( 12 , 7 )?
- What is the image ofA′′?
- PlotA,A′,A′′, andA′′′from the questions above. What do you notice? Write a conjecture.
The vertices of 4 ABCareA(− 6 ,− 7 ),B(− 3 ,− 10 )andC(− 5 , 2 ). Find the vertices of 4 A′B′C′, given the translation
rules below.
9.(x,y)→(x− 2 ,y− 7 )
10.(x,y)→(x+ 11 ,y+ 4 )