http://www.ck12.org Chapter 12. Rigid Transformations
U F=
√
1852 +(− 204 )^2 ∼= 275. 4 miles,PF=√
622 + 912 ∼= 110. 1 milesVocabulary
Atransformationis an operation that moves, flips, or otherwise changes a figure to create a new figure. Arigid
transformation(also known as anisometryorcongruence transformation) is a transformation that does not
change the size or shape of a figure. The new figure created by a transformation is called theimage. The original
figure is called thepreimage. Atranslationis a transformation that moves every point in a figure the same distance
in the same direction. Avectoris a quantity that has direction and size. Thecomponent formof a vector combines
the horizontal distance traveled and the vertical distance traveled.
Guided Practice
- Find the translation rule for 4 T RIto 4 T′R′I′.
- Draw the vector
⇀
STwith component form〈 2 ,− 5 〉.- Triangle 4 ABChas coordinatesA( 3 ,− 1 ),B( 7 ,− 5 )andC(− 2 ,− 2 ). Translate 4 ABCusing the vector〈− 4 , 5 〉.
Determine the coordinates of 4 A′B′C′. - 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 ).
Practice
- 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 )?