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Diketahui A(−1, 5, 4), B(2, −1, −2) dan C(3, p, q). Jika titik-titik A, B, dan C segaris, tentukan nilai  dan q.

Pertanyaan

Diketahui straight A open parentheses negative 1 comma space 5 comma space 4 close parenthesesstraight B open parentheses 2 comma space minus 1 comma space minus 2 close parentheses dan straight C open parentheses 3 comma space p comma space q close parentheses. Jika titik-titik A, B, dan C segaris, tentukan nilai p dan q.

D. Rajib

Master Teacher

Mahasiswa/Alumni Universitas Muhammadiyah Malang

Jawaban terverifikasi

Jawaban

nilai padalah negative 3 dan q adalah negative 4.

Pembahasan

Karena titik-titik A, B, dan C segaris maka berlaku stack text AB end text with rightwards arrow on top equals k times stack text AC end text with rightwards arrow on top.

table attributes columnalign right center left columnspacing 0px end attributes row cell stack text AB end text with rightwards arrow on top end cell equals cell straight B minus straight A end cell row blank equals cell open parentheses table row 2 row cell negative 1 end cell row cell negative 2 end cell end table close parentheses minus open parentheses table row cell negative 1 end cell row 5 row 4 end table close parentheses end cell row blank equals cell open parentheses table row cell 2 plus 1 end cell row cell negative 1 minus 5 end cell row cell negative 2 minus 4 end cell end table close parentheses end cell row blank equals cell open parentheses table row 3 row cell negative 6 end cell row cell negative 6 end cell end table close parentheses end cell end table 

table attributes columnalign right center left columnspacing 0px end attributes row cell stack text AC end text with rightwards arrow on top end cell equals cell straight C minus straight A end cell row blank equals cell open parentheses table row 3 row p row q end table close parentheses minus open parentheses table row cell negative 1 end cell row 5 row 4 end table close parentheses end cell row blank equals cell open parentheses table row cell 3 plus 1 end cell row cell p minus 5 end cell row cell q minus 4 end cell end table close parentheses end cell row blank equals cell open parentheses table row 4 row cell p minus 5 end cell row cell q minus 4 end cell end table close parentheses end cell end table 

Akibatnya diperoleh :

table attributes columnalign right center left columnspacing 0px end attributes row cell stack text AB end text with rightwards arrow on top end cell equals cell k times stack text AC end text with rightwards arrow on top end cell row cell open parentheses table row 3 row cell negative 6 end cell row cell negative 6 end cell end table close parentheses end cell equals cell k open parentheses table row 4 row cell p minus 5 end cell row cell q minus 4 end cell end table close parentheses end cell row cell open parentheses table row 3 row cell negative 6 end cell row cell negative 6 end cell end table close parentheses end cell equals cell open parentheses table row cell 4 k end cell row cell open parentheses p minus 5 close parentheses k end cell row cell open parentheses q minus 4 close parentheses k end cell end table close parentheses end cell end table 

table attributes columnalign right center left columnspacing 0px end attributes row 3 equals cell 4 k end cell row k equals cell 3 over 4 end cell end table 

table attributes columnalign right center left columnspacing 0px end attributes row cell negative 6 end cell equals cell k open parentheses p minus 5 close parentheses end cell row cell negative 6 end cell equals cell 3 over 4 open parentheses p minus 5 close parentheses end cell row cell negative 24 end cell equals cell 3 p minus 15 end cell row cell negative 24 plus 15 end cell equals cell 3 p end cell row cell negative 9 end cell equals cell 3 p end cell row p equals cell negative 3 end cell row blank blank blank row cell negative 6 end cell equals cell k open parentheses q minus 4 close parentheses end cell row cell negative 6 end cell equals cell 3 over 4 open parentheses q minus 4 close parentheses end cell row cell negative 24 end cell equals cell 3 q minus 12 end cell row cell negative 24 plus 12 end cell equals cell 3 q end cell row cell negative 12 end cell equals cell 3 q end cell row q equals cell negative 4 end cell end table 

Dengan demikian, nilai padalah negative 3 dan q adalah negative 4.

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