Roboguru

Diketahui titik  dan . Panjang vektor  adalah ....

Pertanyaan

Diketahui titik straight A open parentheses 2 comma space 5 close parentheses dan straight B open parentheses negative 1 comma space 2 close parentheses. Panjang vektor AB adalah ....

  1. 92 

  2. 26 

  3. 18 

  4. 32 

  5. 24 

Pembahasan Soal:

Diketahui titik straight A open parentheses 2 comma space 5 close parentheses dan straight B open parentheses negative 1 comma space 2 close parentheses, maka:

AB with rightwards arrow on top equals straight b with rightwards arrow on top minus straight a with rightwards arrow on top AB with rightwards arrow on top equals open parentheses table row cell negative 1 end cell row 2 end table close parentheses minus open parentheses table row 2 row 5 end table close parentheses AB with rightwards arrow on top equals open parentheses table row cell negative 3 end cell row cell negative 3 end cell end table close parentheses 

Sehingga:

open vertical bar AB with rightwards arrow on top close vertical bar equals square root of open parentheses negative 3 close parentheses squared plus open parentheses negative 3 close parentheses squared end root open vertical bar AB with rightwards arrow on top close vertical bar equals square root of 9 plus 9 end root open vertical bar AB with rightwards arrow on top close vertical bar equals square root of 18 open vertical bar AB with rightwards arrow on top close vertical bar equals square root of 9 cross times 2 end root open vertical bar AB with rightwards arrow on top close vertical bar equals 3 square root of 2 

Jadi, jawaban yang benar adalah 3 square root of 2 berarti tidak ada pilihan jawaban yang sesuai.

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

W. Lestari

Mahasiswa/Alumni Universitas Sriwijaya

Terakhir diupdate 06 Juni 2021

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

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Pertanyaan yang serupa

Panjang vektor  adalah ....

Pembahasan Soal:

Jika begin mathsize 14px style a with rightwards arrow on top equals open parentheses table row x row y end table close parentheses end style, maka panjang vektor begin mathsize 14px style a with rightwards arrow on top equals open vertical bar a with rightwards arrow on top close vertical bar equals square root of x squared plus y squared end root end style.

undefined, maka panjang vektor begin mathsize 14px style v with rightwards arrow on top end style:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open vertical bar v with rightwards arrow on top close vertical bar end cell equals cell square root of left parenthesis negative 4 right parenthesis squared plus 6 to the power of 2 end exponent end root end cell row blank equals cell square root of 16 plus 36 end root end cell row blank equals cell square root of 52 end cell row blank equals cell square root of 4 times 13 end root end cell row blank equals cell 2 square root of 13 end cell row blank blank blank end table end style
 

Oleh karena itu, jawaban yang benar adalah C.

0

Roboguru

Panjang vektor  adalah ....

Pembahasan Soal:

Ingat kembali:

straight a with rightwards arrow on top equals open parentheses table row cell straight x subscript 1 end cell row cell straight y subscript 1 end cell end table close parentheses rightwards arrow open vertical bar straight a with rightwards arrow on top close vertical bar equals square root of straight x subscript 1 squared plus straight y subscript 1 squared end root 

Diketahui straight v with rightwards arrow on top equals open parentheses table row cell negative 2 end cell row 4 end table close parentheses, maka:

open vertical bar straight v with rightwards arrow on top close vertical bar equals square root of open parentheses negative 2 close parentheses squared plus 4 squared end root open vertical bar straight v with rightwards arrow on top close vertical bar equals square root of 4 plus 16 end root open vertical bar straight v with rightwards arrow on top close vertical bar equals square root of 20 open vertical bar straight v with rightwards arrow on top close vertical bar equals square root of 4 cross times 5 end root open vertical bar straight v with rightwards arrow on top close vertical bar equals 2 square root of 5 

Jadi, jawaban yang benar adalah C.

0

Roboguru

Panjang vektor adalah

Pembahasan Soal:

Rumus panjang vektor begin mathsize 14px style straight a with rightwards arrow on top equals open vertical bar straight a with rightwards arrow on top close vertical bar equals square root of straight x squared plus straight y squared end root end style dengan vektor begin mathsize 14px style straight a with rightwards arrow on top equals open parentheses table row straight x row straight y end table close parentheses end style. Sehingga,

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open vertical bar straight v with rightwards arrow on top close vertical bar end cell equals cell square root of open parentheses negative 4 close parentheses squared plus 6 squared end root end cell row blank equals cell square root of 16 plus 36 end root end cell row blank equals cell square root of 52 end cell row blank equals cell 2 square root of 13 end cell end table end style

Jadi, jawaban yang tepat adalah C.

0

Roboguru

Panjang vektor  adalah ....

Pembahasan Soal:

Jika begin mathsize 14px style a with rightwards arrow on top equals open parentheses table row x row y end table close parentheses end style, maka panjang vektornya adalah begin mathsize 14px style open vertical bar a with rightwards arrow on top close vertical bar equals square root of x squared plus y squared end root end style.

begin mathsize 14px style v with rightwards arrow on top equals open parentheses table row cell negative 4 end cell row 6 end table close parentheses end style, panjang vektornya:
 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open vertical bar v with rightwards arrow on top close vertical bar end cell equals cell square root of left parenthesis negative 4 right parenthesis squared plus 6 to the power of 2 end exponent end root end cell row blank equals cell square root of 16 plus 36 end root end cell row blank equals cell square root of 52 end cell row blank equals cell 2 square root of 13 end cell end table end style
 

Oleh karena itu, jawaban yang benar adalah C.

0

Roboguru

Diketahui segitiga dengan titik-titik sudut . Tentukanlah keliling segitiga !

Pembahasan Soal:

Apabila segitiga PQR digambarkan akan membentuk gambar sebagai berikut:

Berdasarkan soal diketahui titik-titik sudut straight P left parenthesis negative 7 comma negative 3 right parenthesis comma space straight Q left parenthesis 7 comma negative 3 right parenthesis comma space dan space straight R left parenthesis 2 comma 9 right parenthesis, sehingga:

table attributes columnalign right center left columnspacing 0px end attributes row straight P equals cell open parentheses table row cell negative 7 end cell row cell negative 3 end cell end table close parentheses end cell row straight Q equals cell open parentheses table row 7 row cell negative 3 end cell end table close parentheses end cell row straight R equals cell open parentheses table row 2 row 9 end table close parentheses end cell end table

Maka,

table attributes columnalign right center left columnspacing 0px end attributes row cell PQ with rightwards arrow on top end cell equals cell straight q with rightwards arrow on top minus straight p with rightwards arrow on top end cell row blank equals cell open parentheses table row 7 row cell negative 3 end cell end table close parentheses minus open parentheses table row cell negative 7 end cell row cell negative 3 end cell end table close parentheses end cell row blank equals cell open parentheses table row 14 row 0 end table close parentheses end cell row cell open vertical bar PQ close vertical bar end cell equals cell square root of 14 squared end root end cell row blank equals 14 end table

table attributes columnalign right center left columnspacing 0px end attributes row cell PR with rightwards arrow on top end cell equals cell straight r with rightwards arrow on top minus straight p with rightwards arrow on top end cell row blank equals cell open parentheses table row 2 row 9 end table close parentheses minus open parentheses table row cell negative 7 end cell row cell negative 3 end cell end table close parentheses end cell row blank equals cell open parentheses table row 9 row 12 end table close parentheses end cell row cell open vertical bar PR close vertical bar end cell equals cell square root of 9 squared plus 12 squared end root end cell row blank equals cell square root of 81 plus 144 end root end cell row blank equals cell square root of 225 end cell row blank equals 15 end table

table attributes columnalign right center left columnspacing 0px end attributes row cell QR with rightwards arrow on top end cell equals cell straight r with rightwards arrow on top minus straight q with rightwards arrow on top end cell row blank equals cell open parentheses table row 2 row 9 end table close parentheses minus open parentheses table row 7 row cell negative 3 end cell end table close parentheses end cell row blank equals cell open parentheses table row cell negative 5 end cell row 12 end table close parentheses end cell row cell open vertical bar QR close vertical bar end cell equals cell square root of open parentheses negative 5 close parentheses squared plus 12 squared end root end cell row blank equals cell square root of 25 plus 144 end root end cell row blank equals cell square root of 169 end cell row blank equals 13 end table

Jadi, keliling segitiga PQR adalah

table attributes columnalign right center left columnspacing 0px end attributes row Keliling equals cell 14 plus 15 plus 13 end cell row blank equals 42 end table

0

Roboguru

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

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