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Parabola y=x2−2 direfleksikan ke garis y=−2x, petanya adalah ...

Pertanyaan

Parabola y equals x squared minus 2 direfleksikan ke garis y equals negative 2 x, petanya adalah ...

  1. 9 x squared plus 16 y squared plus 24 x y plus 20 x plus 15 y plus 50 equals 0

  2. 9 x squared plus 16 y squared plus 24 x y plus 20 x plus 15 y minus 50 equals 0

  3. 9 x squared plus 16 y squared plus 24 x y plus 20 x minus 15 y minus 50 equals 0 

  4. 9 x squared plus 16 y squared plus 24 x y minus 20 x minus 15 y minus 50 equals 0

  5. 9 x squared plus 16 y squared minus 24 x y minus 20 x plus 15 y minus 50 equals 0

H. Eka

Master Teacher

Mahasiswa/Alumni Universitas Pendidikan Indonesia

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah C.

Pembahasan

Jika titik open parentheses a comma space b close parentheses direfleksikan ke garis y equals m x dan petanya open parentheses a apostrophe comma space b apostrophe close parentheses, maka:

open parentheses table row cell a apostrophe end cell row cell b apostrophe end cell end table close parentheses equals fraction numerator 1 over denominator 1 plus m squared end fraction open parentheses table row cell open parentheses 1 minus m squared close parentheses end cell cell 2 m end cell row cell 2 m end cell cell negative open parentheses 1 minus m squared close parentheses end cell end table close parentheses open parentheses table row a row b end table close parentheses

Diketahui parabola y equals x squared minus 2 direfleksikan ke garis y equals negative 2 x.

Misal open parentheses x comma space y close parentheses adalah titik pada y equals x squared minus 2 dan petanya open parentheses x apostrophe comma space y apostrophe close parentheses, 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 fraction numerator 1 over denominator 1 plus open parentheses negative 2 close parentheses squared end fraction open parentheses table row cell 1 minus open parentheses negative 2 close parentheses squared end cell cell 2 open parentheses negative 2 close parentheses end cell row cell 2 open parentheses negative 2 close parentheses end cell cell negative open parentheses 1 minus open parentheses negative 2 close parentheses squared close parentheses 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 cell negative 4 end cell row cell negative 4 end cell 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 negative 4 over 5 end cell row cell negative 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 end table

Untuk menentukan open parentheses x comma space y close parentheses, gunakan sifat persamaan matriks berikut.

A X equals B space rightwards double arrow space X equals A to the power of negative 1 end exponent B

dengan A to the power of negative 1 end exponent equals fraction numerator 1 over denominator open vertical bar A close vertical bar end fraction times text Adj end text space A 

Akan ditentukan open parentheses x comma space y close parentheses sebagai berikut.

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 negative 3 over 5 end cell cell negative 4 over 5 end cell row cell negative 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 x row y end table close parentheses end cell equals cell open parentheses table row cell negative 3 over 5 end cell cell negative 4 over 5 end cell row cell negative 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 row blank equals cell fraction numerator 1 over denominator open parentheses negative begin display style 3 over 5 end style times begin display style 3 over 5 end style close parentheses minus open parentheses negative begin display style 4 over 5 end style times open parentheses negative begin display style 4 over 5 end style close parentheses close parentheses end fraction open parentheses table row cell 3 over 5 end cell cell 4 over 5 end cell row cell 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 row blank equals cell fraction numerator 1 over denominator negative begin display style 9 over 25 end style minus begin display style 16 over 25 end style end fraction open parentheses table row cell 3 over 5 end cell cell 4 over 5 end cell row cell 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 row blank equals cell fraction numerator 1 over denominator negative 1 end fraction open parentheses table row cell 3 over 5 end cell cell 4 over 5 end cell row cell 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 row blank equals cell open parentheses table row cell negative 3 over 5 end cell cell negative 4 over 5 end cell row cell negative 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 row blank equals cell open parentheses table row cell negative 3 over 5 x apostrophe minus 4 over 5 y apostrophe end cell row cell negative 4 over 5 x apostrophe plus 3 over 5 y apostrophe end cell end table close parentheses end cell end table

Diperoleh x equals negative 3 over 5 x apostrophe minus 4 over 5 y apostrophe dan y equals negative 4 over 5 x apostrophe plus 3 over 5 y apostrophe sehingga peta dari parabola dapat ditentukan sebagai berikut.

table attributes columnalign right center left columnspacing 0px end attributes row y equals cell x squared minus 2 end cell row cell negative 4 over 5 x apostrophe plus 3 over 5 y apostrophe end cell equals cell open parentheses negative 3 over 5 x apostrophe minus 4 over 5 y apostrophe close parentheses squared minus 2 end cell row cell negative 4 over 5 x apostrophe plus 3 over 5 y apostrophe end cell equals cell 9 over 25 x apostrophe squared plus 24 over 25 x apostrophe y apostrophe plus 16 over 25 y apostrophe squared minus 2 end cell row cell negative 20 x apostrophe plus 15 y apostrophe end cell equals cell 9 x apostrophe squared plus 24 x apostrophe y apostrophe plus 16 y apostrophe squared minus 50 end cell row 0 equals cell 9 x squared plus 16 y squared plus 24 x y plus 20 x minus 15 y minus 50 end cell end table

Peta parabola di atas adalah 9 x squared plus 16 y squared plus 24 x y plus 20 x minus 15 y minus 50 equals 0 

Oleh karena itu, jawaban yang tepat adalah C.

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