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Jika P(−2, 2, 4) dan Q(−4, −2, 2), buktikan bahwa △POQ merupakan segitiga sama sisi.

Pertanyaan

Jika P open parentheses negative 2 comma space 2 comma space 4 close parentheses dan Q open parentheses negative 4 comma space minus 2 comma space 2 close parentheses, buktikan bahwa increment P O Q merupakan segitiga sama sisi.

D. Rajib

Master Teacher

Mahasiswa/Alumni Universitas Muhammadiyah Malang

Jawaban terverifikasi

Pembahasan

Jawaban yang benar untuk pertanyaan tersebut adalah segitiga sama sisi.

Ingat!

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 rightwards arrow 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 

maka dari itu,

stack O P with rightwards arrow on top equals open parentheses table row cell negative 2 end cell row 2 row 4 end table close parentheses stack O Q with rightwards arrow on top equals open parentheses table row cell negative 4 end cell row cell negative 2 end cell row 2 end table close parentheses 

maka, dengan begitu

table attributes columnalign right center left columnspacing 0px end attributes row cell stack P Q with rightwards arrow on top end cell equals cell stack O Q with rightwards arrow on top minus stack O P with rightwards arrow on top end cell row blank equals cell open parentheses table row cell negative 4 end cell row cell negative 2 end cell row 2 end table close parentheses minus open parentheses table row cell negative 2 end cell row 2 row 4 end table close parentheses end cell row blank equals cell open parentheses table row cell negative 2 end cell row cell negative 4 end cell row cell negative 2 end cell end table close parentheses end cell end table

dengan menggunakan, konsep besaran vektor,

table attributes columnalign right center left columnspacing 0px end attributes row cell open vertical bar stack O P with rightwards arrow on top close vertical bar end cell equals cell square root of negative 2 squared plus 2 squared plus 4 squared end root end cell row blank equals cell square root of 4 plus 4 plus 16 end root end cell row blank equals cell square root of 24 end cell row blank equals cell 2 square root of 6 end cell row cell open vertical bar stack O Q with rightwards arrow on top close vertical bar end cell equals cell square root of negative 4 squared plus open parentheses negative 2 close parentheses squared plus 2 squared end root end cell row blank equals cell square root of 16 plus 4 plus 4 end root end cell row blank equals cell square root of 24 end cell row blank equals cell 2 square root of 6 end cell row cell open vertical bar stack P Q with rightwards arrow on top close vertical bar end cell equals cell square root of open parentheses negative 2 close parentheses 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 row blank equals cell 2 square root of 6 end cell end table

jadi, triangle P O Q merupakan segitiga sama sisi dengan nilai panjang sisi 2 square root of 6

dengan demikian, triangle P O Q merupakan segitiga sama sisi

27

5.0 (1 rating)

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Jawaban terverifikasi

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