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Tentukan koordinat titik P apabila  membagi AB dengan perbandingan berikut: b. A(2, 4), B(11, 1), dan AP : PB=2 : 1

Pertanyaan

Tentukan koordinat titik begin mathsize 14px style straight P end style apabila begin mathsize 14px style straight P end style membagi begin mathsize 14px style AB end style dengan perbandingan berikut:

b. begin mathsize 14px style straight A open parentheses 2 comma space 4 close parentheses end stylebegin mathsize 14px style straight B open parentheses 11 comma space 1 close parentheses end style, dan begin mathsize 14px style AP space colon space PB equals 2 space colon space 1 end style 

Y. Fathoni

Master Teacher

Mahasiswa/Alumni Universitas Negeri Yogyakarta.

Jawaban terverifikasi

Pembahasan

Gunakan konsep perbandingan vektor.

Ingat bahwa.

begin mathsize 14px style straight A open parentheses x subscript straight A comma space y subscript straight A close parentheses comma space straight B open parentheses x subscript straight B comma space y subscript straight B close parentheses rightwards arrow AB open parentheses table row cell x subscript straight B minus x subscript straight A end cell row cell y subscript straight B minus y subscript straight A end cell end table close parentheses end style 

begin mathsize 14px style Misal space titik space straight P open parentheses x subscript straight P comma space y subscript straight P close parentheses end style.

Perhatikan perhitungan berikut.

begin mathsize 14px style table attributes columnalign right center left columnspacing 2px end attributes row cell AP space colon space PB end cell equals cell 2 space colon space 1 end cell row cell AP over PB end cell equals cell 2 over 1 end cell row AP equals cell 2 cross times PB end cell row cell open parentheses table row cell x subscript straight P minus x subscript straight A end cell row cell y subscript straight P minus y subscript straight A end cell end table close parentheses end cell equals cell 2 cross times open parentheses table row cell x subscript straight B minus x subscript straight P end cell row cell y subscript straight B minus y subscript straight P end cell end table close parentheses end cell row cell open parentheses table row cell x subscript straight P minus 2 end cell row cell y subscript straight P minus 4 end cell end table close parentheses end cell equals cell 2 cross times open parentheses table row cell 11 minus x subscript straight P end cell row cell 1 minus y subscript straight P end cell end table close parentheses end cell row cell open parentheses table row cell x subscript straight P minus 2 end cell row cell y subscript straight P minus 4 end cell end table close parentheses end cell equals cell open parentheses table row cell 22 minus 2 x subscript straight P end cell row cell 2 minus 2 y subscript straight P end cell end table close parentheses end cell row cell table attributes columnalign right center left columnspacing 2px end attributes row cell x subscript straight P minus 2 end cell equals cell 22 minus 2 x subscript straight P end cell row cell x subscript straight P plus 2 x subscript straight P end cell equals cell 22 plus 2 end cell row cell 3 x subscript straight P end cell equals 24 row cell x subscript straight P end cell equals 8 end table end cell blank cell table attributes columnalign right center left columnspacing 2px end attributes row cell y subscript straight P minus 4 end cell equals cell 2 minus 2 y subscript straight P end cell row cell y subscript straight P plus 2 y subscript straight P end cell equals cell 2 plus 4 end cell row cell 3 y subscript straight P end cell equals 6 row cell y subscript straight P end cell equals 2 end table end cell end table end style   

begin mathsize 14px style Jadi comma space diperoleh space titik space straight P open parentheses 8 comma space 2 close parentheses. end style 

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