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b. Tentukan bayangan titik-titik A ( 0 , 2 ) , B ( 3 ​ , 1 ) , C ( 3 ​ , − 1 ) , D ( − 2 , 0 ) , E ( − 3 ​ , − 1 ) , dan F ( 1 , − 3 ​ ) karena rotasi [ O ( 0 , 0 ) , R ( 3 1 ​ π ) ] .

b. Tentukan bayangan titik-titik , dan  karena rotasi .

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G. Albiah

Master Teacher

Mahasiswa/Alumni Universitas Galuh Ciamis

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bayangan titik-titiknya adalah , , , , , dan .

bayangan titik-titiknya adalah straight A apostrophe left parenthesis square root of 3 comma 1 right parenthesisstraight B apostrophe left parenthesis square root of 3 comma negative 1 right parenthesisstraight C apostrophe left parenthesis 0 comma negative 2 right parenthesisstraight D apostrophe left parenthesis negative 1 comma negative square root of 3 right parenthesisstraight E apostrophe left parenthesis negative square root of 3 comma negative 1 right parenthesis, dan straight F apostrophe left parenthesis 0 comma 2 right parenthesis.

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Pembahasan

Transformasi rotasi ., Maka, 1. 2. 3. 4. 5. , 6. Jadi, bayangan titik-titiknya adalah , , , , , dan .

Transformasi rotasi begin mathsize 14px style straight R open parentheses 1 third straight pi close parentheses end style.,

table attributes columnalign right center left columnspacing 0px end attributes row cell 1 third straight pi end cell equals cell 180 over 3 end cell row blank equals 60 end table

Maka,

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses table row cell x apostrophe end cell row cell y apostrophe end cell end table close parentheses end cell equals cell open parentheses table row cell cos space 60 space end cell cell sin space 60 end cell row cell negative sin space 60 end cell cell cos space 60 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 apostrophe end cell row cell y 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 x row y end table close parentheses end cell end table
 

1. begin mathsize 14px style straight A left parenthesis 0 comma space 2 right parenthesis end style

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses table row cell x apostrophe end cell row cell y apostrophe end cell end table close parentheses end cell equals cell open parentheses table row cell cos space 60 space end cell cell sin space 60 end cell row cell negative sin space 60 end cell cell cos space 60 end cell end table close parentheses open parentheses table row x row cell y apostrophe end cell end table close parentheses end cell row cell open parentheses table row cell x apostrophe end cell row cell y 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 0 row 2 end table close parentheses end cell row blank equals cell open parentheses table row cell 2 open parentheses 1 half square root of 3 close parentheses end cell row cell 2 open parentheses 1 half close parentheses end cell end table close parentheses end cell row blank equals cell open parentheses table row cell square root of 3 end cell row 1 end table close parentheses end cell end table

2. begin mathsize 14px style straight B left parenthesis square root of 3 comma space 1 right parenthesis end style

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses table row cell x apostrophe end cell row cell y apostrophe end cell end table close parentheses end cell equals cell open parentheses table row cell cos space 60 space end cell cell sin space 60 end cell row cell negative sin space 60 end cell cell cos space 60 end cell end table close parentheses open parentheses table row cell square root of 3 end cell row 1 end table close parentheses end cell row cell open parentheses table row cell x apostrophe end cell row cell y 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 square root of 3 end cell row 1 end table close parentheses end cell row blank equals cell open parentheses table row cell 1 half times square root of 3 plus 1 half square root of 3 times 1 end cell row cell negative 1 half square root of 3 times square root of 3 plus 1 half times 1 end cell end table close parentheses end cell row blank equals cell open parentheses table row cell 1 half square root of 3 plus 1 half square root of 3 end cell row cell negative 3 over 2 plus 1 half end cell end table close parentheses end cell row blank equals cell open parentheses table row cell square root of 3 end cell row cell negative 1 end cell end table close parentheses end cell end table

3.begin mathsize 14px style straight C left parenthesis square root of 3 comma space minus 1 right parenthesis end style

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses table row cell x apostrophe end cell row cell y apostrophe end cell end table close parentheses end cell equals cell open parentheses table row cell cos space 60 space end cell cell sin space 60 end cell row cell negative sin space 60 end cell cell cos space 60 end cell end table close parentheses open parentheses table row cell square root of 3 end cell row cell negative 1 end cell end table close parentheses end cell row cell open parentheses table row cell x apostrophe end cell row cell y 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 square root of 3 end cell row cell negative 1 end cell end table close parentheses end cell row blank equals cell open parentheses table row cell 1 half times square root of 3 plus 1 half square root of 3 times negative 1 end cell row cell negative 1 half square root of 3 times square root of 3 plus 1 half times negative 1 end cell end table close parentheses end cell row blank equals cell open parentheses table row cell 1 half square root of 3 minus 1 half square root of 3 end cell row cell negative 3 over 2 minus 1 half end cell end table close parentheses end cell row blank equals cell open parentheses table row 0 row cell negative 2 end cell end table close parentheses end cell end table

4.begin mathsize 14px style straight D left parenthesis negative 2 comma space 0 right parenthesis end style

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses table row cell x apostrophe end cell row cell y apostrophe end cell end table close parentheses end cell equals cell open parentheses table row cell cos space 60 space end cell cell sin space 60 end cell row cell negative sin space 60 end cell cell cos space 60 end cell end table close parentheses open parentheses table row cell negative 2 end cell row 0 end table close parentheses end cell row cell open parentheses table row cell x apostrophe end cell row cell y 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 negative 2 end cell row 0 end table close parentheses end cell row blank equals cell open parentheses table row cell 1 half times negative 2 end cell row cell negative 1 half square root of 3 times negative 2 end cell end table close parentheses end cell row blank equals cell open parentheses table row cell negative 1 end cell row cell negative square root of 3 end cell end table close parentheses end cell end table

5.begin mathsize 14px style straight E left parenthesis negative square root of 3 comma space minus 1 right parenthesis end style,

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses table row cell x apostrophe end cell row cell y apostrophe end cell end table close parentheses end cell equals cell open parentheses table row cell cos space 60 space end cell cell sin space 60 end cell row cell negative sin space 60 end cell cell cos space 60 end cell end table close parentheses open parentheses table row cell negative square root of 3 end cell row cell negative 1 end cell end table close parentheses end cell row cell open parentheses table row cell x apostrophe end cell row cell y 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 negative square root of 3 end cell row cell negative 1 end cell end table close parentheses end cell row blank equals cell open parentheses table row cell open parentheses 1 half times negative square root of 3 close parentheses plus open parentheses 1 half square root of 3 times negative 1 close parentheses end cell row cell open parentheses negative 1 half square root of 3 times negative square root of 3 close parentheses plus open parentheses 1 half times negative 1 close parentheses end cell end table close parentheses end cell row blank equals cell open parentheses table row cell negative 1 half square root of 3 minus 1 half square root of 3 end cell row cell 3 over 2 minus 1 half end cell end table close parentheses end cell row blank equals cell open parentheses table row cell negative square root of 3 end cell row 1 end table close parentheses end cell end table

6.begin mathsize 14px style straight F left parenthesis 1 comma space minus square root of 3 right parenthesis end style

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses table row cell x apostrophe end cell row cell y apostrophe end cell end table close parentheses end cell equals cell open parentheses table row cell cos space 60 space end cell cell sin space 60 end cell row cell negative sin space 60 end cell cell cos space 60 end cell end table close parentheses open parentheses table row cell negative square root of 3 end cell row 1 end table close parentheses end cell row cell open parentheses table row cell x apostrophe end cell row cell y 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 negative square root of 3 end cell row 1 end table close parentheses end cell row blank equals cell open parentheses table row cell open parentheses 1 half times negative square root of 3 close parentheses plus open parentheses 1 half square root of 3 times 1 close parentheses end cell row cell open parentheses negative 1 half square root of 3 times negative square root of 3 close parentheses plus open parentheses 1 half times 1 close parentheses end cell end table close parentheses end cell row blank equals cell open parentheses table row cell negative 1 half square root of 3 plus 1 half square root of 3 end cell row cell 3 over 2 plus 1 half end cell end table close parentheses end cell row blank equals cell open parentheses table row 0 row 2 end table close parentheses end cell end table
 

Jadi, bayangan titik-titiknya adalah straight A apostrophe left parenthesis square root of 3 comma 1 right parenthesisstraight B apostrophe left parenthesis square root of 3 comma negative 1 right parenthesisstraight C apostrophe left parenthesis 0 comma negative 2 right parenthesisstraight D apostrophe left parenthesis negative 1 comma negative square root of 3 right parenthesisstraight E apostrophe left parenthesis negative square root of 3 comma negative 1 right parenthesis, dan straight F apostrophe left parenthesis 0 comma 2 right parenthesis.

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