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Tentukan persamaan bayangan dari setiap rotasi berikut: a. garis l≡2x+y+3=0 dirotasikan terhadap A(−1,2) sejauh 2π​ berlawanan arah jarum jam.

Pertanyaan

Tentukan persamaan bayangan dari setiap rotasi berikut:

a. garis begin mathsize 14px style l identical to 2 x plus y plus 3 equals 0 end style dirotasikan terhadap begin mathsize 14px style A left parenthesis minus sign 1 comma 2 right parenthesis end style sejauh begin mathsize 14px style straight pi over 2 end style berlawanan arah jarum jam.

G. Albiah

Master Teacher

Mahasiswa/Alumni Universitas Galuh Ciamis

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bayangan persamaan garisnya adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank x end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank apostrophe end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank plus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 2 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank y end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank apostrophe end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 2 end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 0 end table.

Pembahasan

Rotasi terhadap  A left parenthesis minus sign 1 comma 2 right parenthesis sejauh begin mathsize 14px style straight pi end style berlawanan jarum jam maka,

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses table row cell x apostrophe end cell row cell y apostrophe end cell end table close parentheses end cell equals cell open parentheses table row cell cos space 90 end cell cell negative sin space 90 end cell row cell sin 90 end cell cell cos space 90 end cell end table close parentheses open parentheses table row cell x minus left parenthesis negative 1 right parenthesis end cell row cell y minus 2 end cell end table close parentheses plus open parentheses table row cell negative 1 end cell row 2 end table close parentheses end cell row cell open parentheses table row cell x apostrophe end cell row cell y apostrophe end cell end table close parentheses end cell equals cell open parentheses table row cell cos space 90 end cell cell negative sin space 90 end cell row cell sin 90 end cell cell cos space 90 end cell end table close parentheses open parentheses table row cell x plus 1 end cell row cell y minus 2 end cell end table close parentheses plus open parentheses table row cell negative 1 end cell row 2 end table close parentheses end cell row cell open parentheses table row cell x apostrophe end cell row cell y apostrophe end cell end table close parentheses end cell equals cell open parentheses table row 0 cell negative 1 end cell row 1 0 end table close parentheses open parentheses table row cell x plus 1 end cell row cell y minus 2 end cell end table close parentheses plus open parentheses table row cell negative 1 end cell row 2 end table close parentheses end cell row cell open parentheses table row cell x apostrophe end cell row cell y apostrophe end cell end table close parentheses end cell equals cell open parentheses table row cell negative 1 left parenthesis y minus 2 right parenthesis end cell row cell 1 left parenthesis x plus 1 right parenthesis end cell end table close parentheses plus open parentheses table row cell negative 1 end cell row 2 end table close parentheses end cell row cell open parentheses table row cell x apostrophe end cell row cell y apostrophe end cell end table close parentheses end cell equals cell open parentheses table row cell negative y plus 2 end cell row cell x plus 1 end cell end table close parentheses plus open parentheses table row cell negative 1 end cell row 2 end table close parentheses end cell row cell open parentheses table row cell x apostrophe end cell row cell y apostrophe end cell end table close parentheses end cell equals cell open parentheses table row cell negative y plus 1 end cell row cell x plus 3 end cell end table close parentheses end cell row cell x apostrophe end cell equals cell negative y plus 1 end cell row y equals cell negative x apostrophe plus 1 end cell row y equals cell 1 minus x apostrophe end cell row blank blank blank row cell y apostrophe end cell equals cell x plus 3 end cell row x equals cell y apostrophe minus 3 end cell end table

Maka di dapat x equals y apostrophe minus 3 dan y equals 1 minus x apostrophe masukkan ke persamaan garis

table attributes columnalign right center left columnspacing 0px end attributes row cell 2 x plus y plus 3 end cell equals 0 row cell 2 left parenthesis y apostrophe minus 3 right parenthesis plus left parenthesis 1 minus x apostrophe right parenthesis plus 3 end cell equals 0 row cell 2 y apostrophe minus 6 plus 1 minus x apostrophe plus 3 end cell equals 0 row cell negative x apostrophe plus 2 y apostrophe minus 2 end cell equals 0 end table
 

Jadi, bayangan persamaan garisnya adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank x end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank apostrophe end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank plus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 2 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank y end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank apostrophe end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 2 end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 0 end table.

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