12.3. Geometric Translations http://www.ck12.org
Thecomponent formof
⇀
ABcombines the horizontal distance traveled and the vertical distance traveled. We writethe component form of
⇀
ABas〈 3 , 7 〉because⇀
ABtravels 3 units to the right and 7 units up. Notice the brackets are
pointed,〈 3 , 7 〉, not curved.
Example A
Graph squareS( 1 , 2 ),Q( 4 , 1 ),R( 5 , 4 )andE( 2 , 5 ). Find the image after the translation(x,y)→(x− 2 ,y+ 3 ). Then,
graph and label the image.
The translation notation tells us that we are going to move the square to the left 2 and up 3.
(x,y)→(x− 2 ,y+ 3 )
S( 1 , 2 )→S′(− 1 , 5 )
Q( 4 , 1 )→Q′( 2 , 4 )
R( 5 , 4 )→R′( 3 , 7 )
E( 2 , 5 )→E′( 0 , 8 )Example B
Name the vector and write its component form.
The vector is
⇀
DC. From the initial pointDto terminal pointC, you would move 6 units to the left and 4 units up.The component form of
⇀
DCis〈− 6 , 4 〉.Example C
Name the vector and write its component form.
The vector is
⇀
EF. The component form of⇀
EFis〈 4 , 1 〉.Watch this video for help with the Examples above.
MEDIA
Click image to the left for more content.CK-12 Foundation: Chapter12TranslationsB
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.