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Diketahui  dan koordinat titik N. Koordinat titik M adalah ....

Pertanyaan

Diketahui begin mathsize 14px style MN with rightwards arrow on top equals left parenthesis 6 comma negative 3 right parenthesis end style dan koordinat titik Nbegin mathsize 14px style left parenthesis 3 comma negative 2 right parenthesis end style. Koordinat titik M adalah ....

Pembahasan Video:

Pembahasan Soal:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell MN with rightwards arrow on top end cell equals cell straight N minus straight M end cell row cell left parenthesis 6 comma negative 3 right parenthesis end cell equals cell left parenthesis 3 minus straight x comma negative 2 minus straight y right parenthesis end cell row cell straight M left parenthesis straight x comma straight y right parenthesis end cell equals cell left parenthesis 3 minus 6 comma negative 2 plus 3 right parenthesis end cell row cell straight M left parenthesis straight x comma straight y right parenthesis end cell equals cell left parenthesis negative 3 comma 1 right parenthesis end cell end table end style

Jadi, Koordinat begin mathsize 14px style straight M left parenthesis negative 3 comma 1 right parenthesis end style.

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

F. Freelancer4

Terakhir diupdate 03 Mei 2021

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Pertanyaan yang serupa

Jika vektor  dan vektor . Nilai panjang  adalah

Pembahasan Soal:

Diketahui: straight a with rightwards arrow on top equals open parentheses 4 comma space 3 comma space minus 2 close parentheses space semicolon space straight b with rightwards arrow on top equals open parentheses 2 comma space 5 comma space minus 1 close parentheses

Ditanya: open vertical bar a with rightwards arrow on top plus b with rightwards arrow on top close vertical bar ?

Jawab:

  • Menentukan straight a with rightwards arrow on top plus straight b with rightwards arrow on top.

table attributes columnalign right center left columnspacing 0px end attributes row cell a with rightwards arrow on top plus b with rightwards arrow on top end cell equals cell open parentheses 4 comma space 3 comma space minus 2 close parentheses plus open parentheses 2 comma space 5 comma space minus 1 close parentheses end cell row blank equals cell open parentheses 6 comma space 8 comma space minus 3 close parentheses end cell end table

  • Menentukan open vertical bar a with rightwards arrow on top plus b with rightwards arrow on top close vertical bar

table attributes columnalign right center left columnspacing 0px end attributes row cell open vertical bar a with rightwards arrow on top plus b with rightwards arrow on top close vertical bar end cell equals cell square root of 6 squared plus 8 squared plus open parentheses negative 3 close parentheses squared end root end cell row blank equals cell square root of 36 plus 64 plus 9 end root end cell row blank equals cell square root of 109 end cell end table

Jadi, panjangnya adalah square root of 109

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Roboguru

dan  a.

Pembahasan Soal:

Panjang vektor dapat ditentukan dengan menggunakan rumus jarak dua titik.

x with rightwards arrow on top equals open parentheses table row 3 row cell negative 5 end cell end table close parentheses

table attributes columnalign right center left columnspacing 0px end attributes row cell open vertical bar x with rightwards arrow on top close vertical bar end cell equals cell square root of 3 squared plus open parentheses negative 5 close parentheses squared end root end cell row blank equals cell square root of 9 plus 25 end root end cell row blank equals cell square root of 34 end cell end table

Jadi, panjang vektor open vertical bar x with rightwards arrow on top close vertical bar adalah square root of 34.

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Roboguru

5. Jika   (1)   (2)   (3)    (4)   Pernyataan yang benar adalah...

Pembahasan Soal:

Perhatikan penghitungan berikut!

begin mathsize 14px style a with rightwards arrow on top equals open parentheses table row 2 row cell negative 1 end cell row 3 end table close parentheses space semicolon space b with rightwards arrow on top equals open parentheses table row cell negative 4 end cell row 2 row cell negative 6 end cell end table close parentheses  left parenthesis 1 right parenthesis space open vertical bar a with rightwards arrow on top plus b with rightwards arrow on top close vertical bar a with rightwards arrow on top plus b with rightwards arrow on top equals open parentheses table row 2 row cell negative 1 end cell row 3 end table close parentheses plus open parentheses table row cell negative 4 end cell row 2 row cell negative 6 end cell end table close parentheses equals open parentheses table row cell negative 2 end cell row 1 row cell negative 3 end cell end table close parentheses open vertical bar a with rightwards arrow on top plus b with rightwards arrow on top close vertical bar equals square root of open parentheses negative 2 close parentheses squared plus 1 squared plus open parentheses negative 3 close parentheses squared end root equals square root of 14   left parenthesis 2 right parenthesis space open vertical bar a with rightwards arrow on top close vertical bar colon open vertical bar b with rightwards arrow on top close vertical bar open vertical bar a with rightwards arrow on top close vertical bar equals square root of 2 squared plus open parentheses negative 1 close parentheses squared plus 3 squared end root equals square root of 14 open vertical bar b with rightwards arrow on top close vertical bar equals square root of open parentheses negative 4 close parentheses squared plus 2 squared plus open parentheses negative 6 close parentheses squared end root equals square root of 56 open vertical bar a with rightwards arrow on top close vertical bar colon open vertical bar b with rightwards arrow on top close vertical bar equals square root of 14 colon square root of 56 equals 1 colon 4  left parenthesis 3 right parenthesis space a with rightwards arrow on top bullet b with rightwards arrow on top open parentheses table row 2 row cell negative 1 end cell row 3 end table close parentheses bullet open parentheses table row cell negative 4 end cell row 2 row cell negative 6 end cell end table close parentheses equals 2 open parentheses negative 4 close parentheses plus 2 open parentheses negative 1 close parentheses plus 3 open parentheses negative 6 close parentheses equals negative 28  left parenthesis 4 right parenthesis space a with rightwards arrow on top divided by divided by b with rightwards arrow on top a with rightwards arrow on top equals open parentheses table row 2 row cell negative 1 end cell row 3 end table close parentheses space minus 2 a with rightwards arrow on top equals negative 2 open parentheses table row 2 row cell negative 1 end cell row 3 end table close parentheses space equals open parentheses table row cell negative 4 end cell row 2 row cell negative 6 end cell end table close parentheses equals b with rightwards arrow on top vektor space a with rightwards arrow on top space jika space diperbesar space 2 space satuan space maka space akan space menjadi space vektor space b with rightwards arrow on top comma sehingga space vektor space a with rightwards arrow on top divided by divided by b with rightwards arrow on top  end style 

Pernyataan yang benar adalah (1),(3), dan (4). Jika disesuaikan dengan pilihan jawaban yang tersedia maka penyataan yang sesuai yaitu (1) dan (3).

Oleh karena itu, jawaban yang benar adalah B. undefined 

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Roboguru

Panjang vektor  sama dengan ...

Pembahasan Soal:

Diketahui vektor v with rightwards arrow on top equals open square brackets 12 comma space 16 close square brackets.

Ingat!

Jika vektor a with rightwards arrow on top equals open parentheses table row cell a subscript 1 end cell row cell a subscript 2 end cell end table close parentheses atau a with rightwards arrow on top equals left parenthesis a subscript 1 comma space a subscript 2 right parenthesis maka panjang vektor a with rightwards arrow on top adalah open vertical bar a with rightwards arrow on top close vertical bar equals square root of a subscript 1 squared plus a subscript 2 squared end root.

sehingga:

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 12 squared plus 16 squared end root end cell row blank equals cell square root of 144 plus 256 end root end cell row blank equals cell square root of 400 end cell row blank equals cell 20 space satuan space panjang end cell end table 


Oleh karena itu, jawaban yang tepat adalah C.

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Roboguru

Jika  dan , nilai  adalah ...

Pembahasan Soal:

Diketahui:

Dua buah vektor begin mathsize 14px style straight p with rightwards arrow on top equals open parentheses table row cell negative 3 end cell row 1 end table close parentheses end style dan begin mathsize 14px style straight q with rightwards arrow on top equals open parentheses table row 4 row 2 end table close parentheses end style.

Diperoleh:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open vertical bar straight p with rightwards arrow on top minus straight q with rightwards arrow on top close vertical bar end cell equals cell square root of open parentheses negative 3 minus 4 close parentheses squared plus open parentheses 1 minus 2 close parentheses squared end root end cell row blank equals cell square root of open parentheses negative 7 close parentheses squared plus open parentheses negative 1 close parentheses squared end root end cell row blank equals cell square root of 49 plus 1 end root end cell row blank equals cell square root of 50 end cell row blank equals cell square root of 25 cross times 2 end root end cell row blank equals cell 5 square root of 2 end cell end table end style

Maka, nilai begin mathsize 14px style open vertical bar straight p with rightwards arrow on top minus straight q with rightwards arrow on top close vertical bar end style adalah begin mathsize 14px style 5 square root of 2 end style.

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Roboguru

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