http://www.ck12.org Chapter 12. Rigid Transformations
Solution: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 )
Example 7:Write the translation rule for the vector translation from Example 6.
Solution:To write〈− 4 , 5 〉as a translation rule, it would be(x,y)→(x− 4 ,y+ 5 ).
Know What? Revisited
a)
⇀
PS=〈− 84 , 187 〉,⇀
SU=〈− 39 , 108 〉,⇀
PU=〈− 123 , 295 〉b)
⇀
PF=〈 62 , 91 〉,⇀
U F=〈 185 ,− 204 〉c) You can plug the vector components into the Pythagorean Theorem to find the distances. Paso Robles is closer to
Fresno than Ukiah.
U F=
√
1852 +(− 204 )^2 ∼= 275. 4 miles,PF=√
622 + 912 ∼= 110. 1 milesReview Questions
- 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.