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Buktikan bahwa segitiga KLM dengan koordinat K(2, −3, 2), L(−1, 0, 2), dan M(0, 1, 4) merupakan segitiga siku-siku.

Pertanyaan

Buktikan bahwa segitiga K L M dengan koordinat K open parentheses 2 comma space minus 3 comma space 2 close parentheses, L open parentheses negative 1 comma space 0 comma space 2 close parentheses, dan M open parentheses 0 comma space 1 comma space 4 close parentheses merupakan segitiga siku-siku.

D. Rajib

Master Teacher

Mahasiswa/Alumni Universitas Muhammadiyah Malang

Jawaban terverifikasi

Pembahasan

Jawaban yang benar untuk pertanyaan tersebut adalah segitiga siku-siku

Ingat!

X open parentheses x subscript 1 comma x subscript 2 comma x subscript 3 close parentheses rightwards arrow x with rightwards arrow on top equals open parentheses table row cell x subscript 1 end cell row cell x subscript 2 end cell row cell x subscript 3 end cell end table close parentheses Y open parentheses y subscript 1 comma y subscript 2 comma y subscript 3 close parentheses rightwards arrow y with rightwards arrow on top equals open parentheses table row cell y subscript 1 end cell row cell y subscript 2 end cell row cell y subscript 3 end cell end table close parentheses

maka,

stack X Y with rightwards arrow on top equals y with rightwards arrow on top minus x with rightwards arrow on top

dan

open vertical bar x with rightwards arrow on top close vertical bar equals square root of x subscript 1 squared plus x subscript 2 squared plus x subscript 3 squared end root

dengan seperti itu,

  • table attributes columnalign right center left columnspacing 0px end attributes row cell stack K L with rightwards arrow on top end cell equals cell l with rightwards arrow on top minus k with rightwards arrow on top end cell row blank equals cell open parentheses table row cell negative 1 end cell row 0 row 2 end table close parentheses minus open parentheses table row 2 row cell negative 3 end cell row 2 end table close parentheses end cell row blank equals cell open parentheses table row cell negative 3 end cell row 3 row 0 end table close parentheses end cell end table
  • table attributes columnalign right center left columnspacing 0px end attributes row cell stack L M with rightwards arrow on top end cell equals cell m with rightwards arrow on top minus l with rightwards arrow on top end cell row blank equals cell open parentheses table row 0 row 1 row 4 end table close parentheses minus open parentheses table row cell negative 1 end cell row 0 row 2 end table close parentheses end cell row blank equals cell open parentheses table row 1 row 1 row 2 end table close parentheses end cell end table
  • table attributes columnalign right center left columnspacing 0px end attributes row cell stack M K with rightwards arrow on top end cell equals cell k with rightwards arrow on top minus m with rightwards arrow on top end cell row blank equals cell open parentheses table row 2 row cell negative 3 end cell row 2 end table close parentheses minus open parentheses table row 0 row 1 row 4 end table close parentheses end cell row blank equals cell open parentheses table row 2 row cell negative 4 end cell row cell negative 2 end cell end table close parentheses end cell end table 

maka, nilai besaran vektor

  • table attributes columnalign right center left columnspacing 0px end attributes row cell open vertical bar stack K L with rightwards arrow on top close vertical bar end cell equals cell square root of negative 3 squared plus 3 squared plus 0 squared end root end cell row blank equals cell square root of 9 plus 9 plus 0 end root end cell row blank equals cell square root of 18 end cell end table
  • table attributes columnalign right center left columnspacing 0px end attributes row cell open vertical bar stack L M with rightwards arrow on top close vertical bar end cell equals cell square root of 1 squared plus 1 squared plus 2 squared end root end cell row blank equals cell square root of 1 plus 1 plus 4 end root end cell row blank equals cell square root of 6 end cell end table
  • table attributes columnalign right center left columnspacing 0px end attributes row cell open vertical bar stack M K with rightwards arrow on top close vertical bar end cell equals cell square root of 2 squared plus open parentheses negative 4 close parentheses squared plus open parentheses negative 2 close parentheses squared end root end cell row blank equals cell square root of 4 plus 16 plus 4 end root end cell row blank equals cell square root of 24 end cell end table

table attributes columnalign right center left columnspacing 0px end attributes row cell open vertical bar stack K L with rightwards arrow on top close vertical bar squared plus open vertical bar stack L M with rightwards arrow on top close vertical bar squared end cell equals cell open vertical bar stack M K with rightwards arrow on top close vertical bar squared end cell row cell 18 plus 6 end cell equals 24 end table

maka, triangle K L M adalah segitiga siku-siku

dengan demikian, triangle K L M adalah segitiga siku-siku

66

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