Lingkaran L: x2 + y2= 1 didilatasikan dengan faktor skala −3 terhadap titik pusat (0, 0). kemudian ditranslasikan oleh T=(2−1​). Hasil transformasi lingkaran L mempunyai persamaan...

Pertanyaan

Lingkaran begin mathsize 14px style L colon space x squared space plus space y squared equals space 1 end style didilatasikan dengan faktor skala begin mathsize 14px style negative 3 end style terhadap titik pusat (0, 0). kemudian ditranslasikan oleh begin mathsize 14px style T equals open parentheses table row 2 row cell negative 1 end cell end table close parentheses end style. Hasil transformasi lingkaran L mempunyai persamaan...

  1. begin mathsize 14px style left parenthesis x space minus space 2 right parenthesis squared space plus space left parenthesis y space minus space 1 space right parenthesis squared space equals space 1 end style

  2. size 14px left parenthesis size 14px x size 14px space size 14px minus size 14px space size 14px 2 size 14px right parenthesis to the power of size 14px 2 size 14px space size 14px plus size 14px space size 14px left parenthesis size 14px y size 14px space size 14px plus size 14px space size 14px 1 size 14px space size 14px right parenthesis to the power of size 14px 2 size 14px space size 14px equals size 14px space size 14px 1

  3. size 14px left parenthesis size 14px x size 14px space size 14px plus size 14px space size 14px 2 size 14px right parenthesis to the power of size 14px 2 size 14px space size 14px plus size 14px space size 14px left parenthesis size 14px y size 14px space size 14px minus size 14px space size 14px 1 size 14px space size 14px right parenthesis to the power of size 14px 2 size 14px space size 14px equals size 14px space size 14px 9 

  4. size 14px left parenthesis size 14px x size 14px space size 14px minus size 14px space size 14px 2 size 14px right parenthesis to the power of size 14px 2 size 14px space size 14px plus size 14px space size 14px left parenthesis size 14px y size 14px space size 14px plus size 14px space size 14px 1 size 14px space size 14px right parenthesis to the power of size 14px 2 size 14px space size 14px equals size 14px space size 14px 9

  5. size 14px left parenthesis size 14px x size 14px space size 14px plus size 14px space size 14px 2 size 14px right parenthesis to the power of size 14px 2 size 14px space size 14px plus size 14px space size 14px left parenthesis size 14px y size 14px space size 14px plus size 14px space size 14px 1 size 14px space size 14px right parenthesis to the power of size 14px 2 size 14px space size 14px equals size 14px space size 14px 9

H. Janatu

Master Teacher

Mahasiswa/Alumni Universitas Riau

Jawaban terverifikasi

Jawaban

hasil transformasi lingkaran L adalah D. begin mathsize 14px style begin bold style left parenthesis x minus 2 right parenthesis end style to the power of bold 2 bold plus begin bold style left parenthesis y plus 1 right parenthesis end style to the power of bold 2 bold equals bold 9 end style

Pembahasan

begin mathsize 14px style open parentheses table row cell x to the power of apostrophe end cell row cell y to the power of apostrophe end cell end table close parentheses equals open parentheses table row cell negative 3 end cell 0 row 0 cell negative 3 end cell end table close parentheses open parentheses table row x row y end table close parentheses plus open parentheses table row 2 row cell negative 1 end cell end table close parentheses equals open parentheses table row cell negative 3 x plus 2 end cell row cell negative 3 y minus 1 end cell end table close parentheses end style 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell x to the power of apostrophe end cell equals cell negative 3 x plus 2 end cell row x equals cell fraction numerator x to the power of apostrophe minus 2 over denominator negative 3 end fraction end cell end table end style 

begin mathsize 14px style y to the power of apostrophe equals negative 3 y minus 1 y equals fraction numerator y to the power of apostrophe plus 1 over denominator negative 3 end fraction end style 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell x squared plus y squared end cell equals 1 row cell left parenthesis fraction numerator x to the power of apostrophe minus 2 over denominator negative 3 end fraction right parenthesis squared plus left parenthesis fraction numerator y to the power of apostrophe plus 1 over denominator negative 3 end fraction right parenthesis squared end cell equals 1 row cell left parenthesis x minus 2 right parenthesis squared plus left parenthesis y plus 1 right parenthesis squared end cell equals 9 end table end style 

Jadi, hasil transformasi lingkaran L adalah D. begin mathsize 14px style begin bold style left parenthesis x minus 2 right parenthesis end style to the power of bold 2 bold plus begin bold style left parenthesis y plus 1 right parenthesis end style to the power of bold 2 bold equals bold 9 end style

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