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Pertanyaan

Garis y equals 3 x minus 1 direfleksikan ke garis y equals 2 x petanya adalah ...

  1. 13 x plus 9 y equals 5

  2. 13 x minus 9 y equals 5

  3. 13 x minus 9 y equals negative 5

  4. 9 x minus 13 y equals 5

  5. 9 x plus 13 y equals 5

N. Puspita

Master Teacher

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah C.

Pembahasan

Diketahui: Garis y equals 3 x minus 1 direfleksikan ke garis y equals 2 x

Ditanya: Peta hasil refleksi?

Jawab:

Ingat cara untuk menentukan peta atau refleksi ke garis y equals m x sebagai berikut.

open parentheses table row cell x apostrophe end cell row cell y apostrophe end cell end table close parentheses equals fraction numerator 1 over denominator m squared plus 1 end fraction open parentheses table row cell 1 minus m squared end cell cell 2 m end cell row cell 2 m end cell cell m squared minus 1 end cell end table close parentheses open parentheses table row x row y end table close parentheses

Informasi pada soal diketahui bahwa Garis y equals 3 x minus 1 akan dicerminkan ke garis y equals 2 x yang berarti nilai gradiennya yaitu m equals 2.

Ingat juga cara menentukan invers dari sebuah  matriks yaitu

A equals open parentheses table row a b row c d end table close parentheses rightwards arrow A to the power of negative 1 end exponent equals fraction numerator 1 over denominator a d minus b c end fraction open parentheses table row d cell negative b end cell row cell negative c end cell a end table close parentheses

Dari rumus di atas dengan memperhatikan sifat invers pada matriks yaitu 

A X equals B left right double arrow X equals A to the power of negative 1 end exponent B

Dari rumus di atas maka akan didapatkan

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 fraction numerator 1 over denominator m squared plus 1 end fraction open parentheses table row cell 1 minus m squared end cell cell 2 m end cell row cell 2 m end cell cell m squared minus 1 end cell end table close parentheses open parentheses table row x row y 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 fraction numerator 1 over denominator 2 squared plus 1 end fraction open parentheses table row cell 1 minus 2 squared end cell cell 2 left parenthesis 2 right parenthesis end cell row cell 2 left parenthesis 2 right parenthesis end cell cell 2 squared minus 1 end cell end table close parentheses open parentheses table row x row y 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 fraction numerator 1 over denominator 4 plus 1 end fraction open parentheses table row cell 1 minus 4 end cell 4 row 4 cell 4 minus 1 end cell end table close parentheses open parentheses table row x row y 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 1 fifth open parentheses table row cell negative 3 end cell 4 row 4 3 end table close parentheses open parentheses table row x row y 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 3 over 5 end cell cell 4 over 5 end cell row cell 4 over 5 end cell cell 3 over 5 end cell end table close parentheses open parentheses table row x row y end table close parentheses end cell row cell open parentheses table row cell negative 3 over 5 end cell cell 4 over 5 end cell row cell 4 over 5 end cell cell 3 over 5 end cell end table close parentheses to the power of negative 1 end exponent 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 x row y end table close parentheses end cell row cell fraction numerator 1 over denominator negative 3 over 5 times 3 over 5 minus 4 over 5 times 4 over 5 end fraction open parentheses table row cell 3 over 5 end cell cell negative 4 over 5 end cell row cell negative 4 over 5 end cell cell negative 3 over 5 end cell end table close parentheses 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 x row y end table close parentheses end cell row cell fraction numerator 1 over denominator negative 9 over 25 minus 16 over 25 end fraction open parentheses table row cell 3 over 5 end cell cell negative 4 over 5 end cell row cell negative 4 over 5 end cell cell negative 3 over 5 end cell end table close parentheses 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 x row y end table close parentheses end cell row cell fraction numerator 1 over denominator negative 25 over 25 end fraction open parentheses table row cell 3 over 5 end cell cell negative 4 over 5 end cell row cell negative 4 over 5 end cell cell negative 3 over 5 end cell end table close parentheses 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 x row y end table close parentheses end cell row cell fraction numerator 1 over denominator negative 1 end fraction open parentheses table row cell 3 over 5 end cell cell negative 4 over 5 end cell row cell negative 4 over 5 end cell cell negative 3 over 5 end cell end table close parentheses 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 x row y end table close parentheses end cell row cell negative 1 open parentheses table row cell 3 over 5 end cell cell negative 4 over 5 end cell row cell negative 4 over 5 end cell cell negative 3 over 5 end cell end table close parentheses 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 x row y end table close parentheses end cell row cell open parentheses table row cell negative 3 over 5 end cell cell 4 over 5 end cell row cell 4 over 5 end cell cell 3 over 5 end cell end table close parentheses 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 x row y end table close parentheses end cell row cell open parentheses table row cell negative 3 over 5 x apostrophe plus 4 over 5 y apostrophe end cell row cell 4 over 5 x apostrophe plus 3 over 5 y apostrophe end cell end table close parentheses end cell equals cell open parentheses table row x row y end table close parentheses end cell end table

Didapatkan hasil x equals negative 3 over 5 x apostrophe plus 4 over 5 y apostrophe dan y equals 4 over 5 x apostrophe plus 3 over 5 y apostrophe.

Substitusi hasil x dan y ke persamaan awal y equals 3 x minus 1

table attributes columnalign right center left columnspacing 0px end attributes row y equals cell 3 x minus 1 end cell row cell 4 over 5 x apostrophe plus 3 over 5 y apostrophe end cell equals cell 3 open parentheses negative 3 over 5 x apostrophe plus 4 over 5 y apostrophe close parentheses minus 1 end cell row cell 4 over 5 x apostrophe plus 3 over 5 y apostrophe end cell equals cell negative 9 over 5 x apostrophe plus 12 over 5 y apostrophe minus 1 end cell row cell 4 over 5 x apostrophe plus 3 over 5 y apostrophe end cell equals cell negative 9 over 5 x apostrophe plus 12 over 5 y apostrophe minus 1 horizontal ellipsis left parenthesis dikali blank 5 right parenthesis end cell row cell 4 x apostrophe plus 3 y apostrophe end cell equals cell negative 9 x apostrophe plus 12 y apostrophe minus 5 end cell row cell 4 x apostrophe plus 3 y apostrophe plus 9 x apostrophe minus 12 y apostrophe end cell equals cell negative 5 end cell row cell 13 x apostrophe minus 9 y apostrophe end cell equals cell negative 5 end cell end table

Didapatkan hasil petanya yaitu 13 x minus 9 y equals negative 5.

Jadi, dapat disimpulkan bahwa garis y equals 3 x minus 1 direfleksikan ke garis y equals 2 x mempunyai peta 13 x minus 9 y equals negative 5.

Oleh karena itu, jawaban yang benar adalah C.

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