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Sebuah titik A(x,y) mengalami tiga kali transformasi. Jika M T 1 ​ ​ , M T 2 ​ ​ dan M T 3 ​ ​ berturut-turut menyatakan matriks transformasi pertama, matriks transformasi kedua dan matriks transformasi ketiga maka rumus transfromasinya adalah ….

Sebuah titik A(x,y) mengalami tiga kali transformasi. Jika  dan berturut-turut menyatakan matriks transformasi pertama, matriks transformasi kedua dan matriks transformasi ketiga maka rumus transfromasinya adalah ….

  1. begin mathsize 14px style open parentheses table row cell x to the power of apostrophe apostrophe apostrophe end exponent end cell row cell y to the power of apostrophe apostrophe apostrophe end exponent end cell end table close parentheses equals straight M subscript straight T subscript 1 end subscript times straight M subscript straight T subscript 2 end subscript times straight M subscript straight T subscript 3 end subscript times open parentheses table row x row y end table close parentheses end style 

  2. begin mathsize 14px style open parentheses table row cell x to the power of apostrophe apostrophe apostrophe end exponent end cell row cell y to the power of apostrophe apostrophe apostrophe end exponent end cell end table close parentheses equals straight M subscript straight T subscript 3 end subscript times straight M subscript straight T subscript 2 end subscript times straight M subscript straight T subscript 1 end subscript times open parentheses table row x row y end table close parentheses end style 

  3. begin mathsize 14px style open parentheses table row cell x to the power of apostrophe apostrophe apostrophe end exponent end cell row cell y to the power of apostrophe apostrophe apostrophe end exponent end cell end table close parentheses equals straight M subscript straight T subscript 2 end subscript times straight M subscript straight T subscript 3 end subscript times straight M subscript straight T subscript 1 end subscript times open parentheses table row x row y end table close parentheses end style 

  4. begin mathsize 14px style open parentheses table row cell x to the power of apostrophe apostrophe apostrophe end exponent end cell row cell y to the power of apostrophe apostrophe apostrophe end exponent end cell end table close parentheses equals straight M subscript straight T subscript 3 end subscript times straight M subscript straight T subscript 1 end subscript times straight M subscript straight T subscript 2 end subscript times open parentheses table row x row y end table close parentheses end style 

  5. begin mathsize 14px style open parentheses table row cell x to the power of apostrophe apostrophe apostrophe end exponent end cell row cell y to the power of apostrophe apostrophe apostrophe end exponent end cell end table close parentheses equals straight M subscript straight T subscript 2 end subscript times straight M subscript straight T subscript 1 end subscript times straight M subscript straight T subscript 3 end subscript times open parentheses table row x row y end table close parentheses end style 

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Pembahasan

Misalkan: menyatakan matriks transformasi pertama menyatakan matriks transformasi kedua menyatakan matriks transformasi ketiga Transformasi pertama, Transformasi kedua, Transformasi ketiga, Jadi rumus transformasinya adalah

Misalkan:
begin mathsize 14px style straight M subscript straight T subscript 1 end subscript end style menyatakan matriks transformasi pertama
begin mathsize 14px style straight M subscript straight T subscript 2 end subscript end style menyatakan matriks transformasi kedua
begin mathsize 14px style straight M subscript straight T subscript 3 end subscript end style menyatakan matriks transformasi ketiga

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Transformasi pertama,

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell A to the power of apostrophe end cell equals cell straight M subscript straight T subscript 1 end subscript times A end cell row cell open parentheses table row cell x to the power of apostrophe end cell row cell y apostrophe end cell end table close parentheses end cell equals cell straight M subscript straight T subscript 1 end subscript times open parentheses table row x row y end table close parentheses end cell end table end style

Transformasi kedua,

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell A to the power of apostrophe apostrophe end exponent end cell equals cell straight M subscript straight T subscript 2 end subscript times A apostrophe end cell row cell open parentheses table row cell x to the power of apostrophe apostrophe end exponent end cell row cell y apostrophe apostrophe end cell end table close parentheses end cell equals cell straight M subscript straight T subscript 2 end subscript 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 cell x to the power of apostrophe apostrophe end exponent end cell row cell y apostrophe apostrophe end cell end table close parentheses end cell equals cell straight M subscript straight T subscript 2 end subscript times straight M subscript straight T subscript 1 end subscript times open parentheses table row x row y end table close parentheses end cell end table end style

Transformasi ketiga,

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell A to the power of apostrophe apostrophe apostrophe end exponent end cell equals cell straight M subscript straight T subscript 3 end subscript times A apostrophe apostrophe end cell row cell open parentheses table row cell x to the power of apostrophe apostrophe apostrophe end exponent end cell row cell y apostrophe apostrophe apostrophe end cell end table close parentheses end cell equals cell straight M subscript straight T subscript 3 end subscript times open parentheses table row cell x apostrophe apostrophe end cell row cell y apostrophe apostrophe end cell end table close parentheses end cell row cell open parentheses table row cell x to the power of apostrophe apostrophe apostrophe end exponent end cell row cell y apostrophe apostrophe apostrophe end cell end table close parentheses end cell equals cell straight M subscript straight T subscript 3 end subscript times straight M subscript straight T subscript 2 end subscript times straight M subscript straight T subscript 1 end subscript times open parentheses table row x row y end table close parentheses end cell end table end style 

Jadi rumus transformasinya adalah 

begin mathsize 14px style open parentheses table row cell x to the power of apostrophe apostrophe apostrophe end exponent end cell row cell y to the power of apostrophe apostrophe apostrophe end exponent end cell end table close parentheses equals straight M subscript straight T subscript 3 end subscript times straight M subscript straight T subscript 2 end subscript times straight M subscript straight T subscript 1 end subscript times open parentheses table row x row y end table close parentheses end style 

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