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Diberikan persegi panjang ABCD dengan A ( 2 , 0 ) , B ( 5 , 3 ) , C ( x C ​ , y C ​ ) , dan D ( x D ​ , y D ​ ) . Koordinat titik potong kedua diagonal persegi panjang tersebut adalah E ( 2 3 ​ , 2 7 ​ ) . Jika persegi panjang diputar terhadap titik O ( 0 , 0 ) sejauh 27 0 ∘ searah jarum jam, tuliskanlah: a. koordinat bayangan titik-titik persegi panjang dan titik E .

Diberikan persegi panjang  dengan , dan . Koordinat titik potong kedua diagonal persegi panjang tersebut adalah . Jika persegi panjang undefined diputar terhadap titik  sejauh  searah jarum jam, tuliskanlah:

a. koordinat bayangan titik-titik persegi panjang undefined dan titik .

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O. Rahmawati

Master Teacher

Mahasiswa/Alumni UIN Sunan Gunung Djati Bandung

Jawaban terverifikasi

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Pembahasan

Menentukan titik : diperoleh: dan Jadi, titik . diperoleh: dan Jadi, titik . Menentukan bayangan titik-titik persegi panjang : Titik : Jadi, bayangan titik-titik tersebut adalah .

  • Menentukan titik C space dan space D:

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses fraction numerator x subscript A plus x subscript C over denominator 2 end fraction comma fraction numerator y subscript A plus y subscript C over denominator 2 end fraction close parentheses end cell equals cell open parentheses 3 over 2 comma space 7 over 2 close parentheses end cell row cell open parentheses fraction numerator 2 plus x subscript C over denominator 2 end fraction comma fraction numerator 0 plus y subscript C over denominator 2 end fraction close parentheses end cell equals cell open parentheses 3 over 2 comma space 7 over 2 close parentheses end cell row cell open parentheses fraction numerator 2 plus x subscript C over denominator 2 end fraction comma y subscript C over 2 close parentheses end cell equals cell open parentheses 3 over 2 comma space 7 over 2 close parentheses end cell end table

diperoleh: 

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator 2 plus x subscript C over denominator 2 end fraction end cell equals cell 3 over 2 end cell row cell 2 plus x subscript C end cell equals 3 row cell x subscript C end cell equals 1 end table 

dan

 table attributes columnalign right center left columnspacing 0px end attributes row cell y subscript C over 2 end cell equals cell 7 over 2 end cell row cell y subscript C end cell equals 7 end table

Jadi, titik C left parenthesis 1 comma space 7 right parenthesis.

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses fraction numerator x subscript B plus x subscript D over denominator 2 end fraction comma fraction numerator y subscript B plus y subscript D over denominator 2 end fraction close parentheses end cell equals cell open parentheses 3 over 2 comma space 7 over 2 close parentheses end cell row cell open parentheses fraction numerator 5 plus x subscript D over denominator 2 end fraction comma fraction numerator 3 plus y subscript D over denominator 2 end fraction close parentheses end cell equals cell open parentheses 3 over 2 comma space 7 over 2 close parentheses end cell end table

diperoleh:

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator 5 plus x subscript D over denominator 2 end fraction end cell equals cell 3 over 2 end cell row cell 5 plus x subscript D end cell equals 3 row cell x subscript D end cell equals cell negative 2 end cell end table

dan 

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator 3 plus y subscript D over denominator 2 end fraction end cell equals cell 7 over 2 end cell row cell 3 plus y subscript D end cell equals 7 row cell y subscript D end cell equals 4 end table

Jadi, titik D left parenthesis negative 2 comma space 4 right parenthesis.

  • Menentukan bayangan titik-titik persegi panjang A B C D:

Titik A apostrophe:

begin mathsize 12px style open parentheses table row cell x subscript A apostrophe end cell row cell y subscript A apostrophe end cell end table table row cell x subscript B apostrophe end cell row cell y subscript B apostrophe end cell end table table row cell x subscript C apostrophe end cell row cell y subscript C apostrophe end cell end table table row cell x subscript D apostrophe end cell row cell y subscript D apostrophe end cell end table table row cell x subscript E apostrophe end cell row cell y subscript E apostrophe end cell end table close parentheses equals open parentheses table row cell cos space left parenthesis negative 270 degree right parenthesis end cell cell negative sin space left parenthesis negative 270 degree right parenthesis end cell row cell sin space left parenthesis negative 270 degree right parenthesis end cell cell cos space left parenthesis negative 270 degree right parenthesis end cell end table close parentheses open parentheses table row cell x subscript A end cell row cell y subscript A end cell end table table row cell x subscript B end cell row cell y subscript B end cell end table table row cell x subscript C end cell row cell y subscript C end cell end table table row cell x subscript D end cell row cell y subscript D end cell end table table row cell x subscript E end cell row cell y subscript E end cell end table close parentheses open parentheses table row cell x subscript A apostrophe end cell row cell y subscript A apostrophe end cell end table table row cell x subscript B apostrophe end cell row cell y subscript B apostrophe end cell end table table row cell x subscript C apostrophe end cell row cell y subscript C apostrophe end cell end table table row cell x subscript D apostrophe end cell row cell y subscript D apostrophe end cell end table table row cell x subscript E apostrophe end cell row cell y subscript E apostrophe end cell end table close parentheses equals open parentheses table row 0 cell negative 1 end cell row 1 0 end table close parentheses open parentheses table row 2 5 1 cell negative 2 end cell cell 3 over 2 end cell row 0 3 7 4 cell 7 over 2 end cell end table close parentheses open parentheses table row cell x subscript A apostrophe end cell row cell y subscript A apostrophe end cell end table table row cell x subscript B apostrophe end cell row cell y subscript B apostrophe end cell end table table row cell x subscript C apostrophe end cell row cell y subscript C apostrophe end cell end table table row cell x subscript D apostrophe end cell row cell y subscript D apostrophe end cell end table table row cell x subscript E apostrophe end cell row cell y subscript E apostrophe end cell end table close parentheses equals open parentheses table row 0 cell negative 3 end cell cell negative 7 end cell cell negative 4 end cell row 2 5 1 cell negative 2 end cell end table table row cell negative 7 over 2 end cell row cell 3 over 2 end cell end table close parentheses end style

Jadi, bayangan titik-titik tersebut adalah A apostrophe left parenthesis 0 comma space 2 right parenthesis comma space B apostrophe left parenthesis negative 3 comma space 5 right parenthesis comma space C apostrophe left parenthesis negative 7 comma space 1 right parenthesis comma space D apostrophe left parenthesis negative 4 comma negative 2 right parenthesis comma space E apostrophe open parentheses negative 7 over 2 comma 3 over 2 close parentheses.

 

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