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Diketahui △PQR dengan P(−3,3), Q(4,6), dan R(2,−3). Tentukan bayangan (peta)  yang dirotasikan terhadap titik berat  sejauh 2π​ searah jarum jam.

Pertanyaan

Diketahui begin mathsize 14px style triangle PQR end style dengan begin mathsize 14px style P left parenthesis minus sign 3 comma 3 right parenthesis end stylebegin mathsize 14px style Q left parenthesis 4 comma 6 right parenthesis end style, dan begin mathsize 14px style R left parenthesis 2 comma minus sign 3 right parenthesis end style. Tentukan bayangan (peta) undefined yang dirotasikan terhadap titik berat undefined sejauh begin mathsize 14px style straight pi over 2 end style searah jarum jam.

Pembahasan:

  • Menentukan titik berat segitiga P Q R:

Z left parenthesis a comma b right parenthesis equals open parentheses fraction numerator P subscript x plus Q subscript x plus R subscript x over denominator 2 end fraction comma fraction numerator P subscript y plus Q subscript y plus R subscript y over denominator 2 end fraction close parentheses Z left parenthesis a comma b right parenthesis equals open parentheses fraction numerator left parenthesis negative 3 right parenthesis plus 4 plus 2 over denominator 2 end fraction comma fraction numerator 3 plus 6 plus left parenthesis negative 3 right parenthesis over denominator 2 end fraction close parentheses Z left parenthesis a comma b right parenthesis equals open parentheses 3 over 2 comma 3 close parentheses

Jadi, triangle P Q R dirotasi terhadap Z open parentheses 3 over 2 comma 3 close parentheses sejauh straight pi over 2 searah jarum jam.

  • Menentukan bayangan triangle P Q R:

Titik P':

open parentheses table row cell x subscript p apostrophe end cell row cell y subscript p apostrophe end cell end table close parentheses equals open parentheses table row cell cos space alpha end cell cell negative sin space alpha end cell row cell sin space alpha end cell cell cos space 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 open parentheses table row cell x subscript p apostrophe end cell row cell y subscript p apostrophe end cell end table close parentheses equals open parentheses table row cell cos space open parentheses negative straight pi over 2 close parentheses end cell cell negative sin space open parentheses negative straight pi over 2 close parentheses end cell row cell sin space open parentheses negative straight pi over 2 close parentheses end cell cell cos space open parentheses negative straight pi over 2 close parentheses end cell end table close parentheses open parentheses table row cell negative 3 minus 3 over 2 end cell row cell 3 minus 3 end cell end table close parentheses plus open parentheses table row cell 3 over 2 end cell row 3 end table close parentheses open parentheses table row cell x subscript p apostrophe end cell row cell y subscript p apostrophe end cell end table close parentheses equals open parentheses table row 0 1 row cell negative 1 end cell 0 end table close parentheses open parentheses table row cell negative 3 minus 3 over 2 end cell row cell 3 minus 3 end cell end table close parentheses plus open parentheses table row cell 3 over 2 end cell row 3 end table close parentheses open parentheses table row cell x subscript p apostrophe end cell row cell y subscript p apostrophe end cell end table close parentheses equals open parentheses table row 0 1 row cell negative 1 end cell 0 end table close parentheses open parentheses table row cell negative 9 over 2 end cell row 0 end table close parentheses plus open parentheses table row cell 3 over 2 end cell row 3 end table close parentheses open parentheses table row cell x subscript p apostrophe end cell row cell y subscript p apostrophe end cell end table close parentheses equals open parentheses table row 0 row cell 9 over 2 end cell end table close parentheses plus open parentheses table row cell 3 over 2 end cell row 3 end table close parentheses open parentheses table row cell x subscript p apostrophe end cell row cell y subscript p apostrophe end cell end table close parentheses equals open parentheses table row cell 3 over 2 end cell row cell 15 over 2 end cell end table close parentheses

Titik Q apostrophe:

open parentheses table row cell x subscript Q apostrophe end cell row cell y subscript Q apostrophe end cell end table close parentheses equals open parentheses table row cell cos space alpha end cell cell negative sin space alpha end cell row cell sin space alpha end cell cell cos space 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 open parentheses table row cell x subscript Q apostrophe end cell row cell y subscript Q apostrophe end cell end table close parentheses equals open parentheses table row cell cos space open parentheses negative straight pi over 2 close parentheses end cell cell negative sin space open parentheses negative straight pi over 2 close parentheses end cell row cell sin space open parentheses negative straight pi over 2 close parentheses end cell cell cos space open parentheses negative straight pi over 2 close parentheses end cell end table close parentheses open parentheses table row cell 4 minus 3 over 2 end cell row cell 6 minus 3 end cell end table close parentheses plus open parentheses table row cell 3 over 2 end cell row 3 end table close parentheses open parentheses table row cell x subscript Q apostrophe end cell row cell y subscript Q apostrophe end cell end table close parentheses equals open parentheses table row 0 1 row cell negative 1 end cell 0 end table close parentheses open parentheses table row cell 4 minus 3 over 2 end cell row cell 6 minus 3 end cell end table close parentheses plus open parentheses table row cell 3 over 2 end cell row 3 end table close parentheses open parentheses table row cell x subscript Q apostrophe end cell row cell y subscript Q apostrophe end cell end table close parentheses equals open parentheses table row 0 1 row cell negative 1 end cell 0 end table close parentheses open parentheses table row cell 5 over 2 end cell row 3 end table close parentheses plus open parentheses table row cell 3 over 2 end cell row 3 end table close parentheses open parentheses table row cell x subscript Q apostrophe end cell row cell y subscript Q apostrophe end cell end table close parentheses equals open parentheses table row 3 row cell negative 5 over 2 end cell end table close parentheses plus open parentheses table row cell 3 over 2 end cell row 3 end table close parentheses open parentheses table row cell x subscript Q apostrophe end cell row cell y subscript Q apostrophe end cell end table close parentheses equals open parentheses table row cell 9 over 2 end cell row cell 1 half end cell end table close parentheses

Titik R apostrophe:

open parentheses table row cell x subscript R apostrophe end cell row cell y subscript R apostrophe end cell end table close parentheses equals open parentheses table row cell cos space alpha end cell cell negative sin space alpha end cell row cell sin space alpha end cell cell cos space 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 open parentheses table row cell x subscript R apostrophe end cell row cell y subscript R apostrophe end cell end table close parentheses equals open parentheses table row cell cos space open parentheses negative straight pi over 2 close parentheses end cell cell negative sin space open parentheses negative straight pi over 2 close parentheses end cell row cell sin space open parentheses negative straight pi over 2 close parentheses end cell cell cos space open parentheses negative straight pi over 2 close parentheses end cell end table close parentheses open parentheses table row cell 2 minus 3 over 2 end cell row cell negative 3 minus 3 end cell end table close parentheses plus open parentheses table row cell 3 over 2 end cell row 3 end table close parentheses open parentheses table row cell x subscript R apostrophe end cell row cell y subscript R apostrophe end cell end table close parentheses equals open parentheses table row 0 1 row cell negative 1 end cell 0 end table close parentheses open parentheses table row cell 2 minus 3 over 2 end cell row cell negative 3 minus 3 end cell end table close parentheses plus open parentheses table row cell 3 over 2 end cell row 3 end table close parentheses open parentheses table row cell x subscript R apostrophe end cell row cell y subscript R apostrophe end cell end table close parentheses equals open parentheses table row 0 1 row cell negative 1 end cell 0 end table close parentheses open parentheses table row cell 1 half end cell row cell negative 6 end cell end table close parentheses plus open parentheses table row cell 3 over 2 end cell row 3 end table close parentheses open parentheses table row cell x subscript R apostrophe end cell row cell y subscript R apostrophe end cell end table close parentheses equals open parentheses table row cell negative 6 end cell row cell negative 1 half end cell end table close parentheses plus open parentheses table row cell 3 over 2 end cell row 3 end table close parentheses open parentheses table row cell x subscript R apostrophe end cell row cell y subscript R apostrophe end cell end table close parentheses equals open parentheses table row cell negative 9 over 2 end cell row cell 5 over 2 end cell end table close parentheses

Jadi, bayangan triangle P Q R space adalah P apostrophe open parentheses 3 over 2 comma 15 over 2 close parentheses comma space Q apostrophe open parentheses 9 over 2 comma 1 half close parentheses comma space R apostrophe open parentheses negative 9 over 2 comma space 5 over 2 close parentheses.

Jawaban terverifikasi

Dijawab oleh:

O. Rahmawati

Mahasiswa/Alumni UIN Sunan Gunung Djati Bandung

Terakhir diupdate 06 Oktober 2021

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