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Pertanyaan

Peta dari y equals x squared oleh refleksi y equals 3 x adalah ...

  1. 16 x squared minus 24 x y plus 9 y squared minus 15 x minus 20 y equals 0

  2. 16 x squared minus 24 x y plus 9 y squared minus 15 x plus 20 y equals 0

  3. 16 x squared minus 24 x y plus 9 y squared plus 15 x plus 20 y equals 0

  4. 16 x squared plus 24 x y plus 9 y squared plus 15 x minus 20 y equals 0

  5. 16 x squared minus 24 x y minus 9 y squared plus 15 x minus 20 y equals 0

M. Iqbal

Master Teacher

Mahasiswa/Alumni Universitas Negeri Semarang

Jawaban terverifikasi

Pembahasan

Diketahui: Parabola y equals x squared direfleksikan ke garis y equals 3 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 y equals x squared akan dicerminkan ke garis y equals 3 x yang berarti nilai gradiennya yaitu m equals 3.

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 3 squared plus 1 end fraction open parentheses table row cell 1 minus 3 squared end cell cell 2 left parenthesis 3 right parenthesis end cell row cell 2 left parenthesis 3 right parenthesis end cell cell 3 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 9 plus 1 end fraction open parentheses table row cell 1 minus 9 end cell 6 row 6 cell 9 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 over 10 open parentheses table row cell negative 8 end cell 6 row 6 8 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 8 over 10 end cell cell 6 over 10 end cell row cell 6 over 10 end cell cell 8 over 10 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 8 over 10 end cell cell 6 over 10 end cell row cell 6 over 10 end cell cell 8 over 10 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 8 over 10 times 8 over 10 minus 6 over 10 times 6 over 10 end fraction open parentheses table row cell 8 over 10 end cell cell negative 6 over 10 end cell row cell negative 6 over 10 end cell cell negative 8 over 10 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 64 over 100 minus 36 over 100 end fraction open parentheses table row cell 8 over 10 end cell cell negative 6 over 10 end cell row cell negative 6 over 10 end cell cell negative 8 over 10 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 100 over 100 end fraction open parentheses table row cell 8 over 10 end cell cell negative 6 over 10 end cell row cell negative 6 over 10 end cell cell negative 8 over 10 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 8 over 10 end cell cell negative 6 over 10 end cell row cell negative 6 over 10 end cell cell negative 8 over 10 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 8 over 10 end cell cell negative 6 over 10 end cell row cell negative 6 over 10 end cell cell negative 8 over 10 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 8 over 10 end cell cell 6 over 10 end cell row cell 6 over 10 end cell cell 8 over 10 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 8 over 10 x apostrophe plus 6 over 10 y apostrophe end cell row cell 6 over 10 x apostrophe plus 8 over 10 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 8 over 10 x apostrophe plus 6 over 10 y apostrophe dan y equals 6 over 10 x apostrophe plus 8 over 10 y apostrophe.

Substitusi hasil x dan y ke persamaan awal y equals x squared

table attributes columnalign right center left columnspacing 0px end attributes row y equals cell x squared end cell row cell 6 over 10 x apostrophe plus 8 over 10 y apostrophe end cell equals cell open parentheses negative 8 over 10 x apostrophe plus 6 over 10 y apostrophe close parentheses squared end cell row cell 6 over 10 x apostrophe plus 8 over 10 y apostrophe end cell equals cell 64 over 100 open parentheses x apostrophe close parentheses squared minus 96 over 100 x apostrophe y apostrophe plus 36 over 100 open parentheses y apostrophe close parentheses squared end cell row cell 6 over 10 x apostrophe plus 8 over 10 y apostrophe end cell equals cell 64 over 100 open parentheses x to the power of apostrophe close parentheses squared minus 96 over 100 x apostrophe y apostrophe plus 36 over 100 open parentheses y apostrophe close parentheses squared horizontal ellipsis left parenthesis dikali blank 100 right parenthesis end cell row cell 60 x apostrophe plus 80 y apostrophe end cell equals cell 64 open parentheses x to the power of apostrophe close parentheses squared minus 96 x apostrophe y apostrophe plus 36 open parentheses y apostrophe close parentheses squared end cell row 0 equals cell 64 open parentheses x apostrophe close parentheses squared minus 96 x apostrophe y apostrophe plus 36 open parentheses y apostrophe close parentheses squared minus 60 x apostrophe minus 80 y apostrophe end cell row 0 equals cell 64 open parentheses x apostrophe close parentheses squared minus 96 x apostrophe y apostrophe plus 36 open parentheses y apostrophe close parentheses squared minus 60 x apostrophe minus 80 y apostrophe end cell row 0 equals cell 16 open parentheses x apostrophe close parentheses squared minus 24 x apostrophe y apostrophe plus 9 open parentheses y apostrophe close parentheses squared minus 15 x apostrophe minus 20 y apostrophe end cell end table

Didapatkan hasil petanya yaitu 16 x squared minus 24 x y plus 9 y squared minus 15 x minus 20 y equals 0.

Jadi, dapat disimpulkan bahwa parabola y equals x squared direfleksikan ke garis y equals 3 x mempunyai peta 16 x squared minus 24 x y plus 9 y squared minus 15 x minus 20 y equals 0.

Oleh karena itu, jawaban yang benar adalah A.

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