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Titik dirotasi sebesar 60° searah jarum jam dengan pusat O(0, 0). Bayangan dari titik A adalah ....

Titik Error converting from MathML to accessible text. dirotasi sebesar 60° searah jarum jam dengan pusat O(0, 0). Bayangan dari titik A adalah ....

  1. begin mathsize 14px style A to the power of apostrophe open parentheses square root of 3 plus 2 square root of 6 comma 3 plus 2 square root of 2 close parentheses end style 

  2. begin mathsize 14px style A to the power of apostrophe open parentheses square root of 3 minus 2 square root of 6 comma 3 plus 2 square root of 2 close parentheses end style 

  3. begin mathsize 14px style A to the power of apostrophe open parentheses square root of 3 plus 2 square root of 6 comma negative 3 plus 2 square root of 2 close parentheses end style 

  4. begin mathsize 14px style A to the power of apostrophe open parentheses square root of 3 minus 4 square root of 2 comma 3 plus 2 square root of 2 close parentheses end style

  5. begin mathsize 14px style A to the power of apostrophe open parentheses square root of 3 plus 4 square root of 2 comma negative 3 plus 2 square root of 2 close parentheses end style 

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Y. Laksmi

Master Teacher

Mahasiswa/Alumni Universitas Negeri Semarang

Jawaban terverifikasi

Jawaban

bayangan dari titik A setelah dirotasi menjadi .

bayangan dari titik A setelah dirotasi menjadi begin mathsize 14px style A to the power of apostrophe open parentheses square root of 3 plus 2 square root of 6 comma negative 3 plus 2 square root of 2 close parentheses end style.

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Ingat bahwa titik A(x, y) jika dirotasi dengan sudut rotasi sebesar θ berlawanan arah jarum jam dengan pusat O(0, 0), maka didapat titik bayangan A’(x’,y’) dengan Pada soal diketahui titik . Sehingga . Karena sudutnya adalah 60° searah jarum jam, maka θ = -60°. Karena pusat rotasinya adalah O(0, 0), maka bayangannya adalah A’(x’, y’) dengan Ingat bahwa cos⁡(-x) = cos⁡x dan sin⁡(-x) = -sin⁡x. Sehingga Maka Sehingga bayangan dari titik A setelah dirotasi menjadi .

Ingat bahwa titik A(x, y) jika dirotasi dengan sudut rotasi sebesar θ berlawanan arah jarum jam dengan pusat O(0, 0), maka didapat titik bayangan A’(x’,y’) dengan

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 cos invisible function application theta end cell cell negative sin invisible function application theta end cell row cell sin invisible function application theta end cell cell cos invisible function application theta end cell end table close parentheses open parentheses table row x row y end table close parentheses end style

Pada soal diketahui titik Error converting from MathML to accessible text.. Sehingga begin mathsize 14px style x equals 2 square root of 3 space d a n space y equals 4 square root of 2 end style.
Karena sudutnya adalah 60° searah jarum jam, maka θ = -60°.
Karena pusat rotasinya adalah O(0, 0), maka bayangannya adalah A’(x’, y’) dengan

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell 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 end cell equals cell open parentheses table row cell cos invisible function application theta end cell cell negative sin invisible function application theta end cell row cell sin invisible function application theta end cell cell cos invisible function application theta 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 to the power of apostrophe end cell row cell y to the power of apostrophe end cell end table close parentheses end cell equals cell open parentheses table row cell cos invisible function application open parentheses negative 60 degree close parentheses end cell cell negative sin invisible function application open parentheses negative 60 degree close parentheses end cell row cell sin invisible function application open parentheses negative 60 degree close parentheses end cell cell cos invisible function application open parentheses negative 60 degree close parentheses end cell end table close parentheses open parentheses table row cell 2 square root of 3 end cell row cell 4 square root of 2 end cell end table close parentheses end cell end table end style

Ingat bahwa cos⁡(-x) = cos⁡x dan sin⁡(-x) = -sin⁡x.
Sehingga

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell cos invisible function application open parentheses negative 60 degree close parentheses end cell equals cell cos invisible function application 60 degree equals 1 half end cell row cell sin invisible function application open parentheses negative 60 degree close parentheses end cell equals cell negative sin invisible function application 60 degree equals negative 1 half square root of 3 end cell end table 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 to the power of apostrophe end cell row cell y to the power of apostrophe end cell end table close parentheses end cell equals cell open parentheses table row cell cos invisible function application open parentheses negative 60 degree close parentheses end cell cell negative sin invisible function application open parentheses negative 60 degree close parentheses end cell row cell sin invisible function application open parentheses negative 60 degree close parentheses end cell cell cos invisible function application open parentheses negative 60 degree close parentheses end cell end table close parentheses open parentheses table row cell 2 square root of 3 end cell row cell 4 square root of 2 end cell end table close parentheses end cell row cell 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 end cell equals cell open parentheses table row cell 1 half end cell cell negative open parentheses negative 1 half square root of 3 close parentheses end cell row cell negative 1 half square root of 3 end cell cell 1 half end cell end table close parentheses open parentheses table row cell 2 square root of 3 end cell row cell 4 square root of 2 end cell end table close parentheses end cell row cell 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 end cell equals cell open parentheses table row cell 1 half end cell cell 1 half square root of 3 end cell row cell negative 1 half square root of 3 end cell cell 1 half end cell end table close parentheses open parentheses table row cell 2 square root of 3 end cell row cell 4 square root of 2 end cell end table close parentheses end cell row cell 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 end cell equals cell open parentheses table row cell 1 half open parentheses 2 square root of 3 close parentheses plus 1 half square root of 3 open parentheses 4 square root of 2 close parentheses end cell row cell negative 1 half square root of 3 open parentheses 2 square root of 3 close parentheses plus 1 half open parentheses 4 square root of 2 close parentheses end cell end table close parentheses end cell row cell 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 end cell equals cell open parentheses table row cell square root of 3 plus 2 square root of 6 end cell row cell negative 3 plus 2 square root of 2 end cell end table close parentheses end cell end table end style

Sehingga bayangan dari titik A setelah dirotasi menjadi begin mathsize 14px style A to the power of apostrophe open parentheses square root of 3 plus 2 square root of 6 comma negative 3 plus 2 square root of 2 close parentheses end style.

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