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Diberikan jajargenjang OABC dengan O ( 0 , 0 ) , A ( 2 , 0 ) , B ( 4 , 4 ) , dan C ( 2 , 4 ) . Tuliskan bayangan dari data berikut! c. Garis k ≡ garis AC dirotasi oleh [ B ( 4 , 4 ) , R ( 3 0 ∘ ) ] .

Diberikan jajargenjang  dengan , dan . Tuliskan bayangan dari data berikut!

c. Garis  dirotasi oleh .

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O. Rahmawati

Master Teacher

Mahasiswa/Alumni UIN Sunan Gunung Djati Bandung

Jawaban terverifikasi

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Pembahasan

Menentukan garis : Menentukan bayangan dari garis : Kita akan melakukan dengan cara eliminasi Gauss-Jordan dalam menjawab soal ini. Persamaan matriks Gauss-Jordan: Proses Eliminasi Gauss-Jordan: Hal ini berarti: Kedua persamaan diatas disubstitusikan ke persamaan garis Jadi, persamaan bayangan adalah .

  • Menentukan garis k identical to A C:

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses y minus y subscript 1 close parentheses open parentheses x subscript 2 minus x subscript 1 close parentheses end cell equals cell open parentheses x minus x subscript 1 close parentheses open parentheses y subscript 2 minus y subscript 1 close parentheses end cell row cell open parentheses y minus 0 close parentheses open parentheses 2 minus 2 close parentheses end cell equals cell open parentheses x minus 2 close parentheses open parentheses 4 minus 0 close parentheses end cell row cell left parenthesis y minus 0 right parenthesis open parentheses 0 close parentheses end cell equals cell open parentheses x minus 2 close parentheses open parentheses 4 close parentheses end cell row 0 equals cell 4 x minus 8 end cell row cell 4 x end cell equals 8 row x equals 2 end table

Menentukan bayangan dari garis k identical to A C:

Kita akan melakukan dengan cara eliminasi Gauss-Jordan dalam menjawab soal ini. 

Persamaan matriks Gauss-Jordan:

open parentheses table row cell cos space 30 degree end cell cell negative sin space 30 degree end cell row cell sin space 30 degree end cell cell cos space 30 degree end cell end table vertical ellipsis table row cell x apostrophe minus 4 end cell row cell y apostrophe minus 4 end cell end table close parentheses equals open parentheses table row cell 1 half square root of 3 end cell cell negative 1 half end cell row cell 1 half end cell cell 1 half square root of 3 end cell end table vertical ellipsis table row cell x apostrophe minus 4 end cell row cell y apostrophe minus 4 end cell end table close parentheses

Proses Eliminasi Gauss-Jordan:

left right double arrow open parentheses table row cell 1 half square root of 3 end cell cell negative 1 half end cell row cell 1 half end cell cell 1 half square root of 3 end cell end table vertical ellipsis table row cell x apostrophe minus 4 end cell row cell y apostrophe minus 4 end cell end table close parentheses table row cell fraction numerator 2 over denominator square root of 3 end fraction B subscript 2 end cell row cell fraction numerator 2 over denominator square root of 3 end fraction B subscript 2 end cell end table left right double arrow open parentheses table row 1 cell negative fraction numerator square root of 3 over denominator 3 end fraction end cell row cell fraction numerator square root of 3 over denominator 3 end fraction end cell 1 end table vertical ellipsis table row cell fraction numerator 2 square root of 3 over denominator 3 end fraction x apostrophe minus fraction numerator 8 square root of 3 over denominator 3 end fraction end cell row cell fraction numerator 2 square root of 3 over denominator 3 end fraction y apostrophe minus fraction numerator 8 square root of 3 over denominator 3 end fraction end cell end table close parentheses table row blank row cell negative fraction numerator square root of 3 over denominator 3 end fraction B subscript 1 plus B subscript 2 end cell end table left right double arrow open parentheses table row 1 cell negative fraction numerator square root of 3 over denominator 3 end fraction end cell row 0 cell 4 over 3 end cell end table vertical ellipsis table row cell fraction numerator 2 square root of 3 over denominator 3 end fraction x apostrophe minus fraction numerator 8 square root of 3 over denominator 3 end fraction end cell row cell negative 2 over 3 x apostrophe plus fraction numerator 2 square root of 3 over denominator 3 end fraction y apostrophe plus 8 over 3 minus 8 over 3 square root of 3 end cell end table close parentheses table row blank row cell 3 over 4 B subscript 2 end cell end table left right double arrow open parentheses table row 1 cell negative fraction numerator square root of 3 over denominator 3 end fraction end cell row 0 1 end table vertical ellipsis table row cell fraction numerator 2 square root of 3 over denominator 3 end fraction x apostrophe minus fraction numerator 8 square root of 3 over denominator 3 end fraction end cell row cell negative 1 half x apostrophe plus 1 half square root of 3 y apostrophe plus 2 minus 2 square root of 3 end cell end table close parentheses table row cell fraction numerator square root of 3 over denominator 3 end fraction B subscript 2 plus B subscript 1 end cell row blank end table left right double arrow open parentheses table row 1 0 row 0 1 end table vertical ellipsis table row cell negative fraction numerator square root of 3 over denominator 6 end fraction x apostrophe plus fraction numerator 2 square root of 3 over denominator 3 end fraction x apostrophe plus 1 half y apostrophe minus 2 square root of 3 minus 2 end cell row cell negative 1 half x apostrophe plus 1 half square root of 3 y apostrophe plus 2 minus 2 square root of 3 end cell end table close parentheses

Hal ini berarti:

table attributes columnalign right center left columnspacing 0px end attributes row cell x minus 4 end cell equals cell negative fraction numerator square root of 3 over denominator 6 end fraction x apostrophe plus fraction numerator 2 square root of 3 over denominator 3 end fraction x apostrophe plus 1 half y apostrophe minus 2 square root of 3 minus 2 end cell row x equals cell negative fraction numerator square root of 3 over denominator 6 end fraction x apostrophe plus fraction numerator 2 square root of 3 over denominator 3 end fraction x apostrophe plus 1 half y apostrophe minus 2 square root of 3 plus 2 space... left parenthesis 1 right parenthesis end cell end table

table attributes columnalign right center left columnspacing 0px end attributes row cell y minus 4 end cell equals cell negative 1 half x apostrophe plus 1 half square root of 3 y apostrophe plus 2 minus 2 square root of 3 end cell row y equals cell negative 1 half x apostrophe plus 1 half square root of 3 y apostrophe plus 6 minus 2 square root of 3... left parenthesis 2 right parenthesis end cell end table

Kedua persamaan diatas disubstitusikan ke persamaan garis x minus 2 equals 0

table attributes columnalign right center left columnspacing 0px end attributes row cell x minus 2 end cell equals 0 row cell negative fraction numerator square root of 3 over denominator 6 end fraction x apostrophe plus fraction numerator 2 square root of 3 over denominator 3 end fraction x apostrophe plus 1 half y apostrophe minus 2 square root of 3 plus 2 minus 2 end cell equals 0 row cell negative fraction numerator square root of 3 over denominator 6 end fraction x apostrophe plus fraction numerator 2 square root of 3 over denominator 3 end fraction x apostrophe plus 1 half y apostrophe minus 2 square root of 3 end cell equals 0 end table

Jadi, persamaan bayangan k identical to A C 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 cell fraction numerator square root of 3 over denominator 6 end fraction end cell 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 cell fraction numerator 2 square root of 3 over denominator 3 end fraction end cell 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 cell 1 half end cell 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 blank cell square root of 3 end cell 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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