http://www.ck12.org Chapter 12. Rigid Transformations
Concept Problem 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 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′.