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Diketahui persamaan garis 4x+3y=12 dan titik P(5, 2). Tentukan panjang AB, PA, dan PB. Catatan: A(5,3−8​) dan B(23​,2)

Pertanyaan

Diketahui persamaan garis 4 x plus 3 y equals 12 dan titik straight P open parentheses 5 comma space 2 close parentheses. Tentukan panjang AB comma space PA comma space dan space PB.

Catatan: straight A open parentheses 5 comma fraction numerator negative 8 over denominator 3 end fraction close parentheses space dan space straight B open parentheses 3 over 2 comma 2 close parentheses

F. Kurnia

Master Teacher

Mahasiswa/Alumni Universitas Jember

Jawaban terverifikasi

Jawaban

 panjang AB comma space PA comma space dan space PB berturut-turut adalah 5 5 over 6 comma space 4 2 over 3 comma space dan space 3 1 half.

Pembahasan

Jawaban yang benar untuk pertanyaan tersebut adalah bold 5 bold 5 over bold 6 bold comma bold space bold 4 bold 2 over bold 3 bold comma bold space bold dan bold space bold 3 bold 1 over bold 2.

Dengan menerapkan teorema pythagoras maka dapat ditentukan panjang AB comma space PA comma space dan space PB adalah

table attributes columnalign right center left columnspacing 0px end attributes row AB equals cell square root of open parentheses straight x subscript straight a minus straight x subscript straight b close parentheses squared plus open parentheses straight y subscript straight a minus straight y subscript straight b close parentheses squared end root end cell row blank equals cell square root of open parentheses 5 minus 3 over 2 close parentheses squared plus open parentheses open parentheses negative 8 over 3 close parentheses minus 2 close parentheses squared end root end cell row blank equals cell square root of open parentheses 7 over 2 close parentheses squared plus open parentheses 14 over 3 close parentheses squared end root end cell row blank equals cell square root of 49 over 4 plus 196 over 9 end root end cell row blank equals cell square root of fraction numerator 441 plus 784 over denominator 36 end fraction end root end cell row blank equals cell 1 over 6 square root of 1225 end cell row blank equals cell 35 over 6 end cell row blank equals cell 5 5 over 6 end cell row PA equals cell square root of open parentheses straight x subscript straight p minus straight x subscript straight a close parentheses squared plus open parentheses straight y subscript straight p minus straight y subscript straight a close parentheses squared end root end cell row blank equals cell square root of open parentheses 5 minus 5 close parentheses squared plus open parentheses 2 minus open parentheses fraction numerator negative 8 over denominator 3 end fraction close parentheses close parentheses squared end root end cell row blank equals cell square root of 0 squared plus open parentheses 14 over 3 close parentheses squared end root end cell row blank equals cell square root of open parentheses 14 over 3 close parentheses squared end root end cell row blank equals cell 14 over 3 end cell row blank equals cell 4 2 over 3 end cell row PB equals cell square root of open parentheses straight x subscript straight p minus straight x subscript straight b close parentheses squared plus open parentheses straight y subscript straight p minus straight y subscript straight b close parentheses squared end root end cell row blank equals cell square root of open parentheses 5 minus 3 over 2 close parentheses squared plus open parentheses 2 minus 2 close parentheses squared end root end cell row blank equals cell square root of open parentheses 7 over 2 close parentheses squared plus 0 squared end root end cell row blank equals cell square root of open parentheses 7 over 2 close parentheses squared end root end cell row blank equals cell 7 over 2 end cell row blank equals cell 3 1 half end cell end table

Dengan demikian, panjang AB comma space PA comma space dan space PB berturut-turut adalah 5 5 over 6 comma space 4 2 over 3 comma space dan space 3 1 half.

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