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Bayangan titik oleh rotasi sejauh berlawanan arah putaran jarum jam, dilanjutkan searah putaran jarum jam terhadap titik pusat adalah ....

Bayangan titik begin mathsize 14px style left parenthesis negative 4 comma 8 right parenthesis end style oleh rotasi sejauh begin mathsize 14px style 50 degree end style berlawanan arah putaran jarum jam, dilanjutkan begin mathsize 14px style 20 degree end style searah putaran jarum jam terhadap titik pusat begin mathsize 14px style O left parenthesis 0 comma 0 right parenthesis end style adalah ....space 

  1. begin mathsize 14px style open parentheses negative 4 plus 2 square root of 3 comma negative 2 plus 4 square root of 3 close parentheses end style 

  2. begin mathsize 14px style open parentheses negative 4 minus 2 square root of 3 comma negative 2 plus 4 square root of 3 close parentheses end style 

  3. begin mathsize 14px style open parentheses 4 plus 2 square root of 3 comma negative 2 plus 4 square root of 3 close parentheses end style 

  4. begin mathsize 14px style open parentheses 4 minus 2 square root of 3 comma 2 plus 4 square root of 3 close parentheses end style 

  5. begin mathsize 14px style open parentheses 4 minus 2 square root of 3 comma 2 minus 4 square root of 3 close parentheses end style 

Jawaban:

Pada rotasi pertama, titik begin mathsize 14px style left parenthesis negative 4 comma 8 right parenthesis end style diputar sebesar begin mathsize 14px style alpha equals 50 degree end style kemudian sebesar begin mathsize 14px style beta equals negative 20 degree end style (bernilai negatif karena diputar searah jarum jam). Sehingga dapat diperoleh bayangan titik setelah dua kali rotasi sebagai berikut

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses table row cell x " end cell row cell y " end cell end table close parentheses end cell equals cell open parentheses table row cell cos open parentheses alpha plus beta close parentheses end cell cell negative sin open parentheses alpha plus beta close parentheses end cell row cell sin open parentheses alpha plus beta close parentheses end cell cell cos open parentheses alpha plus beta close parentheses end cell end table close parentheses open parentheses table row x row y end table close parentheses end cell row blank equals cell open parentheses table row cell cos open parentheses 50 degree plus open parentheses negative 20 degree close parentheses close parentheses end cell cell negative sin open parentheses 50 degree plus open parentheses negative 20 degree close parentheses close parentheses end cell row cell sin open parentheses 50 degree plus open parentheses negative 20 degree close parentheses close parentheses end cell cell cos open parentheses 50 degree plus open parentheses negative 20 degree close parentheses close parentheses end cell end table close parentheses open parentheses table row cell negative 4 end cell row 8 end table close parentheses end cell row blank equals cell open parentheses table row cell cos 30 degree end cell cell negative sin 30 degree end cell row cell sin 30 degree end cell cell cos 30 degree end cell end table close parentheses open parentheses table row cell negative 4 end cell row 8 end table close parentheses end cell row blank equals cell open parentheses table row cell 1 half square root of 3 end cell cell negative 1 half end cell row cell 1 half end cell cell 1 half square root of 3 end cell end table close parentheses open parentheses table row cell negative 4 end cell row 8 end table close parentheses end cell row blank equals cell open parentheses table row cell 1 half square root of 3 open parentheses negative 4 close parentheses plus open parentheses negative 1 half close parentheses open parentheses 8 close parentheses end cell row cell 1 half open parentheses negative 4 close parentheses plus 1 half square root of 3 open parentheses 8 close parentheses end cell end table close parentheses end cell row blank equals cell open parentheses table row cell negative 2 square root of 3 minus 4 end cell row cell negative 2 plus 4 square root of 3 end cell end table close parentheses end cell row blank equals cell open parentheses table row cell negative 4 minus 2 square root of 3 end cell row cell negative 2 plus 4 square root of 3 end cell end table close parentheses end cell end table end style 

Jadi, jawaban yang tepat adalah B. space 

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