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Hitunglah luas △ A B C , jika △ ABC dengan A ( 1 , 1 ) , B ( 7 , 2 ) , dan C ( 3 , 5 ) didilatasi oleh: b. [ ( − 1 , − 5 ) , 4 1 ​ ]

Hitunglah luas , jika  dengan , dan  didilatasi oleh:

b.  

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O. Rahmawati

Master Teacher

Mahasiswa/Alumni UIN Sunan Gunung Djati Bandung

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Pembahasan

Dilatasi dengan pusat dan faktor skala : Menentukan hasil dilatasi : Titik : Titik : Titik : Menentukan luas : Jadi, luas adalah .

Dilatasi dengan pusat P left parenthesis a comma b right parenthesis dan faktor skala k:

open parentheses table row cell x apostrophe end cell row cell y apostrophe end cell end table close parentheses equals open parentheses table row k 0 row 0 k 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

  • Menentukan hasil dilatasi A comma space B comma space dan space C:

Titik A apostrophe:

open parentheses table row cell x subscript A apostrophe end cell row cell y subscript A apostrophe end cell end table close parentheses equals open parentheses table row k 0 row 0 k end table close parentheses open parentheses table row cell x subscript A minus a end cell row cell y subscript A 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 subscript A apostrophe end cell row cell y subscript A apostrophe end cell end table close parentheses equals open parentheses table row cell 1 fourth end cell 0 row 0 cell 1 fourth end cell end table close parentheses open parentheses table row cell 1 minus left parenthesis negative 1 right parenthesis end cell row cell 1 minus left parenthesis negative 5 right parenthesis end cell end table close parentheses plus open parentheses table row cell negative 1 end cell row cell negative 5 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 close parentheses equals open parentheses table row cell 1 fourth end cell 0 row 0 cell 1 fourth end cell end table close parentheses open parentheses table row 2 row 6 end table close parentheses plus open parentheses table row cell negative 1 end cell row cell negative 5 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 close parentheses equals open parentheses table row cell 1 half end cell row cell 3 over 2 end cell end table close parentheses plus open parentheses table row cell negative 1 end cell row cell negative 5 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 close parentheses equals open parentheses table row cell negative 1 half end cell row cell fraction numerator negative 7 over denominator 2 end fraction end cell end table close parentheses

Titik B apostrophe:

open parentheses table row cell x subscript B apostrophe end cell row cell y subscript B apostrophe end cell end table close parentheses equals open parentheses table row k 0 row 0 k end table close parentheses open parentheses table row cell x subscript B minus a end cell row cell y subscript B 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 subscript B apostrophe end cell row cell y subscript B apostrophe end cell end table close parentheses equals open parentheses table row cell 1 fourth end cell 0 row 0 cell 1 fourth end cell end table close parentheses open parentheses table row cell 7 minus left parenthesis negative 1 right parenthesis end cell row cell 2 minus left parenthesis negative 5 right parenthesis end cell end table close parentheses plus open parentheses table row cell negative 1 end cell row cell negative 5 end cell end table close parentheses open parentheses table row cell x subscript B apostrophe end cell row cell y subscript B apostrophe end cell end table close parentheses equals open parentheses table row cell 1 fourth end cell 0 row 0 cell 1 fourth end cell end table close parentheses open parentheses table row 8 row 7 end table close parentheses plus open parentheses table row cell negative 1 end cell row cell negative 5 end cell end table close parentheses open parentheses table row cell x subscript B apostrophe end cell row cell y subscript B apostrophe end cell end table close parentheses equals open parentheses table row 2 row cell 7 over 4 end cell end table close parentheses plus open parentheses table row cell negative 1 end cell row cell negative 5 end cell end table close parentheses open parentheses table row cell x subscript B apostrophe end cell row cell y subscript B apostrophe end cell end table close parentheses equals open parentheses table row 1 row cell negative 13 over 4 end cell end table close parentheses

Titik C apostrophe:

open parentheses table row cell x subscript C apostrophe end cell row cell y subscript C apostrophe end cell end table close parentheses equals open parentheses table row k 0 row 0 k end table close parentheses open parentheses table row cell x subscript C minus a end cell row cell y subscript C 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 subscript C apostrophe end cell row cell y subscript C apostrophe end cell end table close parentheses equals open parentheses table row cell 1 fourth end cell 0 row 0 cell 1 fourth end cell end table close parentheses open parentheses table row cell 3 minus left parenthesis negative 1 right parenthesis end cell row cell 5 minus left parenthesis negative 5 right parenthesis end cell end table close parentheses plus open parentheses table row cell negative 1 end cell row cell negative 5 end cell end table close parentheses open parentheses table row cell x subscript C apostrophe end cell row cell y subscript C apostrophe end cell end table close parentheses equals open parentheses table row cell 1 fourth end cell 0 row 0 cell 1 fourth end cell end table close parentheses open parentheses table row 4 row 10 end table close parentheses plus open parentheses table row cell negative 1 end cell row cell negative 5 end cell end table close parentheses open parentheses table row cell x subscript C apostrophe end cell row cell y subscript C apostrophe end cell end table close parentheses equals open parentheses table row 1 row cell 10 over 4 end cell end table close parentheses plus open parentheses table row cell negative 1 end cell row cell negative 5 end cell end table close parentheses open parentheses table row cell x subscript C apostrophe end cell row cell y subscript C apostrophe end cell end table close parentheses equals open parentheses table row 0 row cell negative 10 over 4 end cell end table close parentheses

  • Menentukan luas triangle A apostrophe B apostrophe C apostrophe:

begin mathsize 12px style straight L triangle straight A apostrophe straight B apostrophe straight C equals 1 half open square brackets open parentheses straight x subscript straight A. straight y subscript straight B plus straight x subscript straight B. straight y subscript straight C plus straight x subscript straight C. straight y subscript straight A close parentheses minus open parentheses straight y subscript straight A. straight x subscript straight B plus straight y subscript straight B. straight x subscript straight C plus straight y subscript straight C. straight x subscript straight A close parentheses close square brackets equals 1 half open square brackets open parentheses straight x subscript straight A. straight y subscript straight B plus straight x subscript straight B. straight y subscript straight C plus straight x subscript straight C. straight y subscript straight A close parentheses minus open parentheses straight y subscript straight A. straight x subscript straight B plus straight y subscript straight B. straight x subscript straight C plus straight y subscript straight C. straight x subscript straight A close parentheses close square brackets equals 1 half open square brackets open parentheses open parentheses negative 1 half close parentheses open parentheses negative 13 over 4 close parentheses plus open parentheses 1 close parentheses open parentheses negative 10 over 4 close parentheses plus open parentheses 0 close parentheses open parentheses fraction numerator negative 7 over denominator 2 end fraction close parentheses close parentheses minus open parentheses open parentheses fraction numerator negative 7 over denominator 2 end fraction close parentheses open parentheses 1 close parentheses plus open parentheses negative 13 over 4 close parentheses open parentheses 0 close parentheses plus open parentheses negative 10 over 4 close parentheses open parentheses negative 1 half close parentheses close parentheses close square brackets equals 1 half open square brackets open parentheses negative 7 over 8 close parentheses minus open parentheses fraction numerator negative 9 over denominator 4 end fraction close parentheses close square brackets equals 1 half open parentheses 11 over 8 close parentheses equals 11 over 16 space satuan space luas end style

Jadi, luas triangle A apostrophe B apostrophe C space adalah 11 over 16 space satuan space luas.

 

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△ O A B dengan koordinat titik O ( 0 , 0 ) , A ( 3 , 0 ) , dan B ( 1 , 6 ) . Jika △ O A B adalah bayangan segitiga O A B oleh transformasi matriks ( 3 1 ​ 4 2 ​ ) , maka luas adalah .... satuan luas.

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