Roboguru

Diketahui titik ; ; dan . Jika titik-titik tersebut segaris, maka nilai

Pertanyaan

Diketahui titik straight A left parenthesis 1 comma space 3 comma space 2 right parenthesis; straight B left parenthesis 3 comma space y comma space z right parenthesis; dan straight C left parenthesis 7 comma space minus 3 comma space 5 right parenthesis. Jika titik-titik tersebut segaris, maka nilai 3 y minus z equals horizontal ellipsis

  1. negative 2 

  2. negative 1 

  3. 0 

  4. 1 

  5. 2

Pembahasan Soal:

Ditentukan vektor stack A B with rightwards arrow on top dan stack B C with rightwards arrow on top dan didapatkan:

table attributes columnalign right center left columnspacing 0px end attributes row cell stack A B with rightwards arrow on top end cell equals cell B minus A end cell row blank equals cell open parentheses table row 3 row y row z end table close parentheses minus open parentheses table row 1 row 3 row 2 end table close parentheses end cell row blank equals cell open parentheses table row 2 row cell y minus 3 end cell row cell z minus 2 end cell end table close parentheses end cell row blank blank blank row cell stack B C with rightwards arrow on top end cell equals cell C minus B end cell row blank equals cell open parentheses table row 7 row cell negative 3 end cell row 5 end table close parentheses minus open parentheses table row 3 row y row z end table close parentheses end cell row blank equals cell open parentheses table row 4 row cell negative 3 minus y end cell row cell 5 minus z end cell end table close parentheses end cell end table 

Karena titik-titik tersebut segaris, maka:

table attributes columnalign right center left columnspacing 0px end attributes row cell stack A B with rightwards arrow on top end cell equals cell k stack B C with rightwards arrow on top end cell row cell open parentheses table row 2 row cell y minus 3 end cell row cell z minus 2 end cell end table close parentheses end cell equals cell k open parentheses table row 4 row cell negative 3 minus y end cell row cell 5 minus z end cell end table close parentheses end cell end table 

Sehingga didapatkan:

table attributes columnalign right center left columnspacing 0px end attributes row 2 equals cell k open parentheses 4 close parentheses end cell row k equals cell 2 over 4 end cell row k equals cell 1 half end cell row blank blank blank row cell y minus 3 end cell equals cell k open parentheses negative 3 minus y close parentheses end cell row cell y minus 3 end cell equals cell 1 half open parentheses negative 3 minus y close parentheses end cell row cell 2 y minus 6 end cell equals cell negative 3 minus y end cell row cell 2 y plus y end cell equals cell negative 3 plus 6 end cell row cell 3 y end cell equals 3 row y equals cell 3 over 3 end cell row y equals 1 row blank blank blank row blank blank blank row cell z minus 2 end cell equals cell k open parentheses 5 minus z close parentheses end cell row cell z minus 2 end cell equals cell 1 half open parentheses 5 minus z close parentheses end cell row cell 2 z minus 4 end cell equals cell 5 minus z end cell row cell 2 z plus z end cell equals cell 5 plus 4 end cell row cell 3 z end cell equals 9 row z equals cell 9 over 3 end cell row z equals 3 end table  

Nilai 3 y minus z didapatkan:

table attributes columnalign right center left columnspacing 0px end attributes row cell 3 y minus z end cell equals cell 3 open parentheses 1 close parentheses minus 3 end cell row blank equals cell 3 minus 3 end cell row blank equals 0 end table 

Dengan demikian, nilai 3 y minus z equals 0.

Jadi, jawaban yang benar adalah C.

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 19 Mei 2021

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