Garis 3x+2y−6=0  ditransformasi oleh matriks (53​21​) diperoleh bayangan ax+by+c=0 maka nilai a+b+c=…

Pertanyaan

Garis begin mathsize 14px style 3 x plus 2 y minus 6 equals 0 end style  ditransformasi oleh matriks begin mathsize 14px style open parentheses table row 5 2 row 3 1 end table close parentheses end style diperoleh bayangan begin mathsize 14px style a x plus b y plus c equals 0 end style maka nilai begin mathsize 14px style a plus b plus c equals horizontal ellipsis end style 

  1. begin mathsize 14px style 7 end style 

  2. begin mathsize 14px style 3 end style 

  3. begin mathsize 14px style 1 end style 

  4. begin mathsize 14px style negative 3 end style 

  5. begin mathsize 14px style negative 7 end style 

I. Kumaralalita

Master Teacher

Mahasiswa/Alumni Universitas Gadjah Mada

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah E. 

Pembahasan

Suatu titik begin mathsize 14px style left parenthesis x comma y right parenthesis end style yang ditransformasikan dengan matriks begin mathsize 14px style open parentheses table row a b row c d end table close parentheses end style menghasilkan bayangan berupa titik baru begin mathsize 14px style open parentheses x apostrophe comma y apostrophe close parentheses end style.

Diketahui matriks transformasinya adalah begin mathsize 14px style open parentheses table row 5 2 row 3 1 end table close parentheses end style, maka

begin mathsize 14px style 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 a b row c d end table close parentheses times 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 5 2 row 3 1 end table close parentheses times 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 5 2 row 3 1 end table close parentheses to the power of negative 1 end exponent times open parentheses table row cell x apostrophe end cell row cell y apostrophe end cell end table close parentheses end cell row cell open parentheses table row x row y end table close parentheses end cell equals cell fraction numerator 1 over denominator 5 times 1 minus 2 times 3 end fraction times open parentheses table row 1 cell negative 2 end cell row cell negative 3 end cell 5 end table close parentheses times open parentheses table row cell x apostrophe end cell row cell y apostrophe end cell end table close parentheses end cell row cell open parentheses table row x row y end table close parentheses end cell equals cell fraction numerator 1 over denominator 5 minus 6 end fraction times open parentheses table row 1 cell negative 2 end cell row cell negative 3 end cell 5 end table close parentheses times open parentheses table row cell x apostrophe end cell row cell y apostrophe end cell end table close parentheses end cell row cell open parentheses table row x row y end table close parentheses end cell equals cell negative 1 times open parentheses table row 1 cell negative 2 end cell row cell negative 3 end cell 5 end table close parentheses times open parentheses table row cell x apostrophe end cell row cell y apostrophe end cell 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 1 end cell 2 row 3 cell negative 5 end cell end table close parentheses times open parentheses table row cell x apostrophe end cell row cell y apostrophe end cell 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 x apostrophe plus 2 y apostrophe end cell row cell 3 x apostrophe minus 5 y apostrophe end cell end table close parentheses end cell end table end style  

Sehingga kita peroleh begin mathsize 14px style x equals negative x apostrophe plus 2 y apostrophe end style dan begin mathsize 14px style y equals 3 x apostrophe minus 5 y apostrophe end style. Substitusikan ke dalam persamaan garis awal begin mathsize 14px style 3 x plus 2 y minus 6 equals 0 end style.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell 3 x plus 2 y minus 6 end cell equals 0 row cell 3 open parentheses negative x apostrophe plus 2 y apostrophe close parentheses plus 2 open parentheses 3 x apostrophe minus 5 y apostrophe close parentheses minus 6 end cell equals 0 row cell negative 3 x apostrophe plus 6 y apostrophe plus 6 x apostrophe minus 10 y apostrophe minus 6 end cell equals 0 row cell negative 3 x apostrophe plus 6 x apostrophe plus 6 y apostrophe minus 10 y apostrophe minus 6 end cell equals 0 row cell 3 x apostrophe minus 4 y apostrophe minus 6 end cell equals 0 end table end style  

Diperoleh bayangan garis begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank a end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank x end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank plus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank b end table 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 blank plus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank c 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 0 end table table attributes columnalign right center left columnspacing 0px end attributes row blank rightwards arrow blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 3 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank x end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 4 end table 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 blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 6 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 0 end table end style.

 begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell a plus b plus c end cell equals cell 3 plus left parenthesis negative 4 right parenthesis plus left parenthesis negative 6 right parenthesis end cell row blank equals cell 3 minus 4 minus 6 end cell row blank equals cell negative 7 end cell end table end style 

Dengan demikian, nilai dari begin mathsize 14px style a plus b plus c equals negative 7 end style.

Jadi, jawaban yang tepat adalah E. 

277

0.0 (0 rating)

Pertanyaan serupa

Diketahui garis g: 2x−3y+6=0 ditranslasikan oleh T=(5−3​). Hasil translasi garis g mempunyai persamaan ....

375

0.0

Jawaban terverifikasi

RUANGGURU HQ

Jl. Dr. Saharjo No.161, Manggarai Selatan, Tebet, Kota Jakarta Selatan, Daerah Khusus Ibukota Jakarta 12860

Coba GRATIS Aplikasi Roboguru

Coba GRATIS Aplikasi Ruangguru

Download di Google PlayDownload di AppstoreDownload di App Gallery

Produk Ruangguru

Produk Lainnya

Fitur Roboguru

Topik Roboguru

Hubungi Kami

Ruangguru WhatsApp

081578200000

Email info@ruangguru.com

info@ruangguru.com

Contact 02140008000

02140008000

Ikuti Kami

©2022 Ruangguru. All Rights Reserved PT. Ruang Raya Indonesia