Roboguru

Titik , , tentukan jarak AB !

Titik straight A open parentheses 4 comma 210 degree close parentheses, straight B open parentheses 8 comma 150 degree close parentheses, tentukan jarak AB !

Jawaban:

Kita ubah koordinat straight A open parentheses 4 comma 210 degree close parentheses menjadi A apostrophe open parentheses x comma y close parentheses 

untuk space absis table attributes columnalign right center left columnspacing 2px end attributes row x equals cell r times cos space alpha end cell row blank equals cell 4 times cos space 210 degree end cell row blank equals cell 4 times open parentheses negative 1 half square root of 3 close parentheses end cell row blank equals cell negative 2 square root of 3 end cell end table  untuk space ordinat table attributes columnalign right center left columnspacing 2px end attributes row y equals cell r times sin space alpha end cell row blank equals cell 4 times sin space 210 end cell row blank equals cell 4 times open parentheses negative 1 half close parentheses end cell row blank equals cell negative 2 end cell end table  A apostrophe open parentheses negative 2 square root of 3 comma space minus 2 close parentheses 

Kemudian kita ubah koordinat B space open parentheses 8 comma 150 degree close parentheses menjadi B apostrophe open parentheses x comma y close parentheses  

untuk space absis table attributes columnalign right center left columnspacing 2px end attributes row x equals cell r times cos space alpha end cell row blank equals cell 8 times cos space 150 degree end cell row blank equals cell 8 times open parentheses negative 1 half square root of 3 close parentheses end cell row blank equals cell negative 4 square root of 3 end cell end table  untuk space ordinat table attributes columnalign right center left columnspacing 2px end attributes row y equals cell r times sin space alpha end cell row blank equals cell 8 times sin space 150 degree end cell row blank equals cell 8 times open parentheses 1 half close parentheses end cell row blank equals 4 end table  B apostrophe open parentheses negative 4 square root of 3 comma space 4 close parentheses 

Nah, terakhir barulah kita hitung jarak AB sebagai berikut :

table attributes columnalign right center left columnspacing 2px end attributes row cell A B end cell equals cell square root of open parentheses open parentheses negative 4 square root of 3 close parentheses minus open parentheses negative 2 square root of 3 close parentheses close parentheses squared plus open parentheses 4 minus open parentheses negative 2 close parentheses close parentheses squared end root end cell row blank equals cell square root of open parentheses negative 2 square root of 3 close parentheses squared plus 6 squared end root end cell row blank equals cell square root of 12 plus 36 end root end cell row blank equals cell square root of 48 end cell row blank equals cell 4 square root of 3 end cell end table 

Jadi, jarak AB adalah 4 square root of 3 

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