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Pertanyaan

Garis begin mathsize 14px style m colon space 2 x minus 4 y plus 5 equals 0 end style didilatasikan dengan faktor skala begin mathsize 14px style negative 2 end style terhadap titik pusat begin mathsize 14px style left parenthesis 2 comma space minus 1 right parenthesis end style, lalu didilatasikan lagi dengan faktor skala begin mathsize 14px style 2 end style terhadap titik pusat undefined. Hasil dilatasi garis begin mathsize 14px style m end style adalah . . . .

  1.   begin mathsize 14px style x minus 2 y minus 30 equals 0 end style 

  2. begin mathsize 14px style x minus 2 y plus 30 equals 0 end style 

  3. begin mathsize 14px style x plus 2 y minus 30 equals 0 end style 

  4. begin mathsize 14px style 2 x minus 4 y minus 15 equals 0 end style 

  5. begin mathsize 14px style 2 x minus 4 y plus 15 equals 0 end style 

A. Nadhira

Master Teacher

Mahasiswa/Alumni Universitas Negeri Malang

Jawaban terverifikasi

Pembahasan

1) Dilatasi dengan faktor skala begin mathsize 14px style negative 2 end style terhadap titik pusat begin mathsize 14px style left parenthesis 2 comma space minus 1 right parenthesis end style :

begin mathsize 14px style x apostrophe equals a plus k left parenthesis x minus a right parenthesis space space space space equals 2 plus left parenthesis negative 2 right parenthesis left parenthesis x minus 2 right parenthesis space space space space equals 2 minus 2 x plus 4 space space space space equals 6 minus 2 x end style

dan

size 14px y size 14px apostrophe size 14px equals size 14px b size 14px plus size 14px k size 14px left parenthesis size 14px y size 14px minus size 14px b size 14px right parenthesis size 14px space size 14px space size 14px space size 14px space size 14px equals size 14px minus size 14px 1 size 14px plus size 14px left parenthesis size 14px minus size 14px 2 size 14px right parenthesis size 14px left parenthesis size 14px y size 14px plus size 14px 1 size 14px right parenthesis size 14px space size 14px space size 14px space size 14px space size 14px equals size 14px minus size 14px 1 size 14px minus size 14px 2 size 14px y size 14px minus size 14px 2 size 14px space size 14px space size 14px space size 14px space size 14px equals size 14px minus size 14px 3 size 14px minus size 14px 2 size 14px y

diperoleh hasil dilatasi adalah begin mathsize 14px style open parentheses x apostrophe comma y apostrophe close parentheses equals left parenthesis negative 2 x plus 6 comma negative 2 y minus 3 right parenthesis end style.

2) Dilatasi dengan faktor skala begin mathsize 14px style 2 end style terhadap titik pusat begin mathsize 14px style left parenthesis 2 comma space minus 1 right parenthesis end style :

begin mathsize 14px style x apostrophe apostrophe equals a plus k left parenthesis x apostrophe minus a right parenthesis space space space space space equals 2 plus left parenthesis 2 right parenthesis left parenthesis left parenthesis negative 2 x plus 6 right parenthesis minus 2 right parenthesis space space space space space equals 2 plus 2 left parenthesis negative 2 x plus 4 right parenthesis space space space space space equals 2 minus 4 x plus 8 space space space space space equals negative 4 x plus 10 end style

dan

size 14px y size 14px apostrophe size 14px apostrophe size 14px equals size 14px b size 14px plus size 14px k size 14px left parenthesis size 14px y size 14px apostrophe size 14px minus size 14px b size 14px right parenthesis size 14px space size 14px space size 14px space size 14px space size 14px space size 14px equals size 14px minus size 14px 1 size 14px plus size 14px left parenthesis size 14px 2 size 14px right parenthesis size 14px left parenthesis size 14px left parenthesis size 14px minus size 14px 2 size 14px y size 14px minus size 14px 3 size 14px right parenthesis size 14px plus size 14px 1 size 14px right parenthesis size 14px space size 14px space size 14px space size 14px space size 14px space size 14px equals size 14px minus size 14px 1 size 14px plus size 14px 2 size 14px left parenthesis size 14px minus size 14px 2 size 14px y size 14px minus size 14px 2 size 14px right parenthesis size 14px space size 14px space size 14px space size 14px space size 14px space size 14px equals size 14px minus size 14px 1 size 14px minus size 14px 4 size 14px y size 14px minus size 14px 4 size 14px space size 14px space size 14px space size 14px space size 14px space size 14px equals size 14px minus size 14px 4 size 14px y size 14px minus size 14px 5

  Maka diperoleh :

begin mathsize 14px style x double apostrophe equals negative 4 x plus 10 space 4 x equals 10 minus x apostrophe apostrophe space space space x equals fraction numerator 10 minus x apostrophe apostrophe over denominator 4 end fraction end style dan   begin mathsize 14px style y apostrophe apostrophe equals negative 4 y minus 5 4 y equals negative 5 minus y apostrophe apostrophe space space y equals fraction numerator negative 5 minus y apostrophe apostrophe over denominator 4 end fraction end style

Subsitusikan nilai x dan y pada garis begin mathsize 14px style m colon space 2 x minus 4 y plus 5 equals 0 end style

begin mathsize 14px style space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space 2 x minus 4 y plus 5 equals 0 2 open parentheses fraction numerator 10 minus x apostrophe apostrophe over denominator 4 end fraction close parentheses minus 4 open parentheses fraction numerator negative 5 minus y apostrophe apostrophe over denominator 4 end fraction close parentheses plus 5 equals 0 space space space space space space space space space space space space space space space fraction numerator 10 minus x apostrophe apostrophe over denominator 2 end fraction plus 5 plus y apostrophe apostrophe plus 5 equals 0 space space space space space space space space space space 10 minus x apostrophe apostrophe plus 10 plus 2 y apostrophe apostrophe plus 10 equals 0 space space space space space space space space space space space space space space space space space space space space space space space minus x apostrophe apostrophe plus 2 y apostrophe apostrophe plus 30 equals 0 space space space space space space space space space space space space space space space space space space space space space space space space space space space x apostrophe apostrophe minus 2 y apostrophe apostrophe minus 30 equals 0 end style  

Jadi, jawaban yang tepat adalah A.

 

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