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Rotasi kurva y = − 2 x 2 − x + 2 di rotasi dengan pusat (- 2,3 ) dan sudut 27 0 ∘ berlawanan arah jarum jam adalah ….

Rotasi kurva    di rotasi dengan pusat (-2,3) dan sudut    berlawanan arah jarum jam adalah ….

  1. begin mathsize 14px style x equals 2 y squared plus 5 y minus 6 end style 

  2. begin mathsize 14px style x equals 2 y squared minus 5 y minus 6 end style 

  3. begin mathsize 14px style x equals negative 2 y squared plus 5 y minus 6 end style 

  4. begin mathsize 14px style x equals negative 2 y squared plus 5 y plus 6 end style 

  5. begin mathsize 14px style x equals negative 2 y squared minus 5 y minus 6 end style 

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H. Eka

Master Teacher

Mahasiswa/Alumni Universitas Pendidikan Indonesia

Jawaban terverifikasi

Pembahasan

Ingat bahwa rotasi titik A( x , y) dengan sudut α dan pusat P (a , b ) adalah A ' (x ' , y ' ) dengan Sudut berlawanan arah jarum jam, maka α bernilai positif. Sehingga dengan rotasi , titik (x , y ) memiliki bayangan di titik : Maka Substitusikan ke , maka

Ingat bahwa rotasi titik A(x,y) dengan sudut α dan pusat P(a,b) 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 alpha end cell cell negative sin invisible function application alpha end cell row cell sin invisible function application alpha end cell cell cos invisible function application alpha 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    

 

Sudut berlawanan arah jarum jam, maka α bernilai positif.

Sehingga dengan rotasi begin mathsize 14px style R open square brackets P open parentheses negative 2 , 3 close parentheses comma 270 to the power of o close square brackets end style  , titik (x,y) memiliki bayangan di titik :

open parentheses table row cell size 14px x to the power of size 14px apostrophe end cell row cell size 14px y to the power of size 14px apostrophe end cell end table close parentheses size 14px equals open parentheses table row cell size 14px cos size 14px invisible function application size 14px 270 to the power of size 14px o end cell cell size 14px minus size 14px sin size 14px invisible function application size 14px 270 to the power of size 14px o end cell row cell size 14px sin size 14px invisible function application size 14px 270 to the power of size 14px o end cell cell size 14px cos size 14px invisible function application size 14px 270 to the power of size 14px o end cell end table close parentheses open parentheses table row cell size 14px x size 14px minus open parentheses size 14px minus size 14px 2 close parentheses end cell row cell size 14px y size 14px minus size 14px 3 end cell end table close parentheses size 14px plus open parentheses table row cell size 14px minus size 14px 2 end cell row size 14px 3 end table close parentheses open parentheses table row cell size 14px x to the power of size 14px apostrophe end cell row cell size 14px y to the power of size 14px apostrophe end cell end table close parentheses size 14px equals open parentheses table row size 14px 0 size 14px 1 row cell size 14px minus size 14px 1 end cell size 14px 0 end table close parentheses open parentheses table row cell size 14px x size 14px plus size 14px 2 end cell row cell size 14px y size 14px minus size 14px 3 end cell end table close parentheses size 14px plus open parentheses table row cell size 14px minus size 14px 2 end cell row size 14px 3 end table close parentheses open parentheses table row cell size 14px x to the power of size 14px apostrophe end cell row cell size 14px y to the power of size 14px apostrophe end cell end table close parentheses size 14px equals open parentheses table row cell size 14px y size 14px minus size 14px 3 end cell row cell size 14px minus size 14px x size 14px minus size 14px 2 end cell end table close parentheses size 14px plus open parentheses table row cell size 14px minus size 14px 2 end cell row size 14px 3 end table close parentheses open parentheses table row cell size 14px x to the power of size 14px apostrophe end cell row cell size 14px y to the power of size 14px apostrophe end cell end table close parentheses size 14px equals open parentheses table row cell size 14px y size 14px minus size 14px 5 end cell row cell size 14px minus size 14px x size 14px plus size 14px 1 end cell end table close parentheses  

 

 

 

Maka

begin mathsize 14px style table row cell x to the power of apostrophe equals y minus 5 end cell row cell y to the power of apostrophe equals negative x plus 1 end cell end table rightwards arrow table row cell x equals negative y to the power of apostrophe plus 1 end cell row cell y equals x to the power of apostrophe plus 5 end cell end table end style  

 

Substitusikan ke begin mathsize 14px style y equals negative 2 x squared minus x plus 2 end style , maka

table attributes columnalign right center left columnspacing 0px end attributes row size 14px y size 14px equals cell size 14px minus size 14px 2 size 14px x to the power of size 14px 2 size 14px minus size 14px x size 14px plus size 14px 2 end cell row cell size 14px x to the power of size 14px apostrophe size 14px plus size 14px 5 end cell size 14px equals cell size 14px minus size 14px 2 open parentheses size 14px minus size 14px y to the power of size 14px apostrophe size 14px plus size 14px 1 close parentheses to the power of size 14px 2 size 14px minus open parentheses size 14px minus size 14px y to the power of size 14px apostrophe size 14px plus size 14px 1 close parentheses size 14px plus size 14px 2 end cell row cell size 14px x to the power of size 14px apostrophe size 14px plus size 14px 5 end cell size 14px equals cell size 14px minus size 14px 2 open parentheses open parentheses size 14px y to the power of size 14px apostrophe close parentheses to the power of size 14px 2 size 14px minus size 14px 2 size 14px y to the power of size 14px apostrophe size 14px plus size 14px 1 close parentheses size 14px plus size 14px y to the power of size 14px apostrophe size 14px minus size 14px 1 size 14px plus size 14px 2 end cell row cell size 14px x to the power of size 14px apostrophe size 14px plus size 14px 5 end cell size 14px equals cell size 14px minus size 14px 2 open parentheses size 14px y to the power of size 14px apostrophe close parentheses to the power of size 14px 2 size 14px plus size 14px 4 size 14px y to the power of size 14px apostrophe size 14px minus size 14px 2 size 14px plus size 14px y to the power of size 14px apostrophe size 14px minus size 14px 1 size 14px plus size 14px 2 end cell row cell size 14px x to the power of size 14px apostrophe end cell size 14px equals cell size 14px minus size 14px 2 open parentheses size 14px y to the power of size 14px apostrophe close parentheses to the power of size 14px 2 size 14px plus size 14px 5 size 14px y to the power of size 14px apostrophe size 14px minus size 14px 6 end cell row size 14px x size 14px equals cell size 14px minus size 14px 2 size 14px y to the power of size 14px 2 size 14px plus size 14px 5 size 14px y size 14px minus size 14px 6 end cell end table   

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