Kurva K≡y=3x+52x−1​. Kurva K ditranslasi oleh matriks (−12​), kemudian dilanjutkan oleh pencerminan terhadap garis y−2=0. Tuliskan persamaan bayangan kurva .

Pertanyaan

Kurva begin mathsize 14px style straight K identical to y equals fraction numerator 2 x minus 1 over denominator 3 x plus 5 end fraction end style. Kurva begin mathsize 14px style straight K end style ditranslasi oleh matriks begin mathsize 14px style open parentheses table row cell negative 1 end cell row 2 end table close parentheses end style, kemudian dilanjutkan oleh pencerminan terhadap garis begin mathsize 14px style y minus 2 equals 0 end style. Tuliskan persamaan bayangan kurva begin mathsize 14px style straight K end style.

G. Albiah

Master Teacher

Mahasiswa/Alumni Universitas Galuh Ciamis

Jawaban terverifikasi

Jawaban

 persamaan bayangan kurva begin mathsize 14px style straight K end style adalah 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 equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 16 x plus 47 over denominator 3 x plus 8 end fraction end cell end table.

Pembahasan

Kurva begin mathsize 14px style straight K end style ditranslasi oleh matriks begin mathsize 14px style open parentheses table row cell negative 1 end cell row 2 end table close parentheses end style kemudian dilanjutkan oleh pencerminan terhadap garis begin mathsize 14px style y minus 2 equals 0 end style maka,

left parenthesis x comma y right parenthesis rightwards arrow with T open parentheses table row cell negative 1 end cell row 2 end table close parentheses on top left parenthesis x minus 1 comma y plus 2 right parenthesis rightwards arrow with y equals 2 on top open parentheses x minus 1 comma 4 minus y plus 2 close parentheses left parenthesis x comma y right parenthesis rightwards arrow with T open parentheses table row cell negative 1 end cell row 2 end table close parentheses on top left parenthesis x minus 1 comma y plus 2 right parenthesis rightwards arrow with y equals 2 on top open parentheses x minus 1 comma 6 minus y close parentheses

Kemudian  masukkan ke persamaan matriks,

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 x minus 1 end cell row cell 6 minus y end cell end table close parentheses end cell row cell x apostrophe end cell equals cell x minus 1 end cell row x equals cell x apostrophe minus 1 end cell row cell y apostrophe end cell equals cell 6 minus y end cell row y equals cell 6 minus y apostrophe end cell end table

Masukkan ke persamaan kurva,

table attributes columnalign right center left columnspacing 0px end attributes row y equals cell fraction numerator 2 x minus 1 over denominator 3 x plus 5 end fraction end cell row cell 6 minus y apostrophe end cell equals cell fraction numerator 2 left parenthesis x apostrophe plus 1 right parenthesis minus 1 over denominator 3 left parenthesis x apostrophe plus 1 right parenthesis plus 5 end fraction end cell row cell 6 minus y apostrophe end cell equals cell fraction numerator 2 x apostrophe plus 2 minus 1 over denominator 3 x apostrophe plus 3 plus 5 end fraction end cell row cell 6 minus y apostrophe end cell equals cell fraction numerator 2 x apostrophe plus 1 over denominator 3 x apostrophe plus 8 end fraction end cell row cell y apostrophe end cell equals cell 6 minus fraction numerator 2 x apostrophe plus 1 over denominator 3 x apostrophe plus 8 end fraction end cell row cell y apostrophe end cell equals cell fraction numerator 6 left parenthesis 3 x apostrophe plus 8 right parenthesis over denominator 3 x apostrophe plus 8 end fraction minus open parentheses fraction numerator 2 x apostrophe plus 1 over denominator 3 x apostrophe plus 8 end fraction close parentheses end cell row cell y apostrophe end cell equals cell fraction numerator 18 x apostrophe plus 48 minus 2 x apostrophe minus 1 over denominator 3 x apostrophe plus 8 end fraction end cell row cell y apostrophe end cell equals cell fraction numerator 16 x apostrophe plus 47 over denominator 3 x apostrophe plus 8 end fraction end cell end table


Jadi, persamaan bayangan kurva begin mathsize 14px style straight K end style adalah 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 equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 16 x plus 47 over denominator 3 x plus 8 end fraction end cell end table.

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