Diketahui titik A(1,2,3), B(3,3,1) dan C(7,x,y). Jika ketiga titik itu terletak pada sebuah garis lurus, tentukan hasil kali x dan y.

Pertanyaan

$begin mathsize 14px style.... end style$
$undefined$

Pembahasan Soal:

Diketahui:

$begin mathsize 14px style straight A left parenthesis 1 comma 2 comma 3 right parenthesis end style$

$begin mathsize 14px style straight B left parenthesis 3 comma 3 comma 1 right parenthesis end style$

$begin mathsize 14px style straight C left parenthesis 7 comma straight x comma straight y right parenthesis end style$

Ditanya:

$begin mathsize 14px style straight x times straight y end style$ =?

Jawab:

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell AB with rightwards harpoon with barb upwards on top end cell equals cell straight B with rightwards harpoon with barb upwards on top minus straight A with rightwards harpoon with barb upwards on top end cell row blank equals cell open parentheses table row 3 row 3 row 1 end table close parentheses minus open parentheses table row 1 row 2 row 3 end table close parentheses end cell row blank equals cell open parentheses table row 2 row 1 row cell negative 2 end cell end table close parentheses end cell row cell BC with rightwards harpoon with barb upwards on top end cell equals cell straight C with rightwards harpoon with barb upwards on top minus straight B with rightwards harpoon with barb upwards on top end cell row blank equals cell open parentheses table row 7 row straight x row straight y end table close parentheses minus open parentheses table row 3 row 3 row 1 end table close parentheses end cell row blank equals cell open parentheses table row 4 row cell straight x minus 3 end cell row cell straight y minus 1 end cell end table close parentheses end cell row blank blank blank end table end style$

Karena A, B dan C berada dalam satu garis lurus, maka

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell AB with rightwards harpoon with barb upwards on top end cell equals cell straight k BC with rightwards harpoon with barb upwards on top end cell row cell open parentheses table row 2 row 1 row cell negative 2 end cell end table close parentheses end cell equals cell straight k open parentheses table row 4 row cell straight x minus 3 end cell row cell straight y minus 1 end cell end table close parentheses end cell row blank left right double arrow cell 2 equals 4 straight k end cell row straight k equals cell 2 over 4 equals 1 half end cell row blank left right double arrow cell 1 equals 1 half times open parentheses straight x minus 3 close parentheses end cell row 2 equals cell straight x minus 3 end cell row 5 equals straight x row blank left right double arrow cell negative 2 equals 1 half times open parentheses straight y minus 1 close parentheses end cell row cell negative 4 end cell equals cell straight y minus 1 end cell row cell negative 3 end cell equals straight y end table end style$

Maka hasil kali x dan y adalah $begin mathsize 14px style straight x times straight y equals 5 times open parentheses negative 3 close parentheses equals negative 15 end style$ .

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 06 Maret 2021

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