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Pertanyaan

Titik A(8, 5) dirotasi dengan sudut rotasi sebesar θ berlawanan arah jarum jam dengan pusat P(2, 1). Bayangan dari titik A adalah A’(x’,y’) dengan ....

  1. 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 6 row 4 end table close parentheses minus open parentheses table row 2 row 1 end table close parentheses end style 

  2. 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 6 row 4 end table close parentheses plus open parentheses table row 2 row 1 end table close parentheses end style 

  3. 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 10 row 6 end table close parentheses minus open parentheses table row 2 row 1 end table close parentheses end style 

  4. 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 10 row 6 end table close parentheses plus open parentheses table row 2 row 1 end table close parentheses end style 

  5. 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 10 row 4 end table close parentheses minus open parentheses table row 2 row 1 end table close parentheses end style 

Y. Laksmi

Master Teacher

Mahasiswa/Alumni Universitas Negeri Semarang

Jawaban terverifikasi

Pembahasan

Ingat bahwa titik A(x,y) jika dirotasi dengan sudut rotasi sebesar θ berlawanan arah jarum jam dengan pusat P(a, b), 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 cell x minus a end cell row cell y minus b end cell end table close parentheses plus open parentheses table row a row b end table close parentheses end style

Pada soal diketahui titik A(8,5). Sehingga x = 8 dan y = 5.
Kemudian pusat rotasinya adalah P(2,1). Sehingga a = 2 dan b = 1.
Karena sudut rotasinya adalah θ, maka bayangannya adalah 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 cell x minus a end cell row cell y minus b end cell end table close parentheses plus open parentheses table row a row b end table close parentheses 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 cell 8 minus 2 end cell row cell 5 minus 1 end cell end table close parentheses plus open parentheses table row 2 row 1 end table close parentheses 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 6 row 4 end table close parentheses plus open parentheses table row 2 row 1 end table close parentheses end style 

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