Parabola y=x2−2 direfleksikan ke garis y=−2x mempunyai peta ...

Pertanyaan

Parabola $y=x^2-2$ direfleksikan ke garis $y=-2x$ mempunyai peta ...

M. Iqbal

Master Teacher

Mahasiswa/Alumni Universitas Negeri Semarang

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah C.

Pembahasan

Diketahui: Parabola y equals x squared minus 2 direfleksikan ke garis y equals negative 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 Parabola y equals x squared minus 2 akan dicerminkan ke garis y equals negative 2 x yang berarti nilai gradiennya yaitu m equals negative 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 left parenthesis negative 2 right parenthesis squared plus 1 end fraction open parentheses table row cell 1 minus left parenthesis negative 2 right parenthesis squared end cell cell 2 left parenthesis negative 2 right parenthesis end cell row cell 2 left parenthesis negative 2 right parenthesis end cell cell left parenthesis negative 2 right parenthesis 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 cell negative 4 end cell row cell negative 4 end cell 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 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 row 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 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 open parentheses negative 4 over 5 close parentheses times open parentheses negative 4 over 5 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 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 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 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 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 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 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 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 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 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 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 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 minus 4 over 5 y apostrophe end cell row cell negative 4 over 5 x to the power of 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 minus 4 over 5 y apostrophe dan y equals negative 4 over 5 x apostrophe plus 3 over 5 y apostrophe .

Substitusi hasil dan ke persamaan awal y equals x squared minus 2

Didapatkan hasil petanya yaitu 9 x squared plus 16 y squared plus 24 x y plus 20 x minus 15 y minus 50 equals 0 .

Jadi, dapat disimpulkan bahwa parabola y equals x squared minus 2 direfleksikan ke garis y equals negative 2 x mempunyai peta 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 benar adalah C.