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Jika dan berturut-turut adalah vektor posisi titik-titik sudut jajargenjang PQRS, dengan PQ sejajar SR, maka  sama dengan ...

Pertanyaan

Jika straight p with rightwards arrow on top comma space straight q with rightwards arrow on top comma space straight r with rightwards arrow on top dan straight s with rightwards arrow on top berturut-turut adalah vektor posisi titik-titik sudut jajargenjang PQRS, dengan PQ sejajar SR, maka straight p with rightwards arrow on top sama dengan ...

  1. negative straight q with rightwards arrow on top plus straight r with rightwards arrow on top plus straight s with rightwards arrow on top

  2. negative straight q with rightwards arrow on top minus straight r with rightwards arrow on top plus straight s with rightwards arrow on top

  3. straight q with rightwards arrow on top minus straight r with rightwards arrow on top plus straight s with rightwards arrow on top

  4. straight q with rightwards arrow on top plus straight r with rightwards arrow on top plus straight s with rightwards arrow on top

  5. straight r with rightwards arrow on top minus straight r with rightwards arrow on top minus straight s with rightwards arrow on top

Pembahasan Soal:

Ingatlah bahwa Vektor Posisi adalah vektor yang berpangkal di pusat koordinat straight O open parentheses 0 comma space 0 close parentheses dan berujung di suatu titik misalkan straight A open parentheses straight x comma space straight y close parentheses. Notasi vektor posisi adalah OA with rightwards arrow on top.

Selanjutnya, mIsalkan terdapat dua buah vektor posisi OA with rightwards arrow on top equals straight a with rightwards arrow on top dan Ob with rightwards arrow on top equals straight b with rightwards arrow on top. Vektor AB dapat didefinisikan sebagai:

AB with rightwards arrow on top equals OB with rightwards arrow on top minus OA with rightwards arrow on top equals straight b with rightwards arrow on top minus straight a with rightwards arrow on top.

Diketahui vektor posisi:

  • OP with rightwards arrow on top equals straight p with rightwards arrow on top
  • OQ with rightwards arrow on top equals straight q with rightwards arrow on top
  • OR with rightwards arrow on top equals straight r with rightwards arrow on top
  • OS with rightwards arrow on top equals straight s with rightwards arrow on top

Pada jajar genjang PQRS, PQ sejajar SR maka panjang sisi keduanya sama besar, begitu juga dengan vektornya. Sehingga:

table attributes columnalign right center left columnspacing 0px end attributes row cell PQ with rightwards arrow on top end cell equals cell SR with rightwards arrow on top end cell row cell straight q with rightwards arrow on top minus straight p with rightwards arrow on top end cell equals cell straight r with rightwards arrow on top minus straight s with rightwards arrow on top end cell row cell negative straight p with rightwards arrow on top end cell equals cell negative straight q with rightwards arrow on top plus straight r with rightwards arrow on top minus straight s with rightwards arrow on top end cell row cell straight p with rightwards arrow on top end cell equals cell straight q with rightwards arrow on top minus straight r with rightwards arrow on top plus straight s with rightwards arrow on top end cell end table

Dengan demikian, table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell straight p with rightwards arrow on top end cell end table sama dengan table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell straight p with rightwards arrow on top end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell straight q with rightwards arrow on top end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell straight r with rightwards arrow on top end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank plus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell straight s with rightwards arrow on top end cell end table.

Oleh karena itu, jawaban yang benar adalah C.

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

D. Nuryani

Mahasiswa/Alumni Universitas Padjadjaran

Terakhir diupdate 11 Juli 2021

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

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Pertanyaan yang serupa

Jarak titik  dengan titik  sama dengan ...

Pembahasan Soal:

Rumus jarak titik A equals open parentheses a comma space b comma space c close parentheses dengan B equals left parenthesis d comma space e comma space f right parenthesis adalah :

AB equals square root of open parentheses d bond a close parentheses squared plus open parentheses e bond b close parentheses to the power of 2 end exponent plus open parentheses f bond c close parentheses squared end root 

Dengan menggunakan rumus jarak titik, maka didapatkan :

table attributes columnalign right center left columnspacing 0px end attributes row CD equals cell square root of left parenthesis 12 minus sign 3 right parenthesis squared plus left parenthesis 0 minus sign left parenthesis minus sign 2 right parenthesis right parenthesis squared plus left parenthesis minus sign 2 minus sign 4 right parenthesis squared end root end cell row blank equals cell square root of 9 squared plus 2 squared plus left parenthesis minus sign 6 right parenthesis squared end root end cell row blank equals cell square root of 81 plus 4 plus 36 end root end cell row blank equals cell square root of 121 end cell row blank equals 11 end table

Maka, jarak kedua titik tersebut adalah 11.

Oleh karena itu, jawaban yang benar adalah C.

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Roboguru

Diketahui  dan vektor . Koordinat titik  yang memenuhi adalah ...

Pembahasan Soal:

Dengan menggunakan sifat vektor, maka didapatkan :

table attributes columnalign right center left columnspacing 0px end attributes row cell KL with bar on top end cell equals cell L bond K end cell row cell open square brackets 3 comma space minus sign 1 comma space 2 close square brackets end cell equals cell open parentheses 4 comma space 5 comma space 1 close parentheses minus sign K end cell row K equals cell open parentheses 4 comma space 5 comma space 1 close parentheses minus sign open square brackets 3 comma space minus sign 1 comma space 2 close square brackets end cell row blank equals cell open parentheses 4 minus sign 3 comma space 5 minus sign left parenthesis minus sign 1 right parenthesis comma space 1 minus sign 2 close parentheses end cell row blank equals cell open parentheses 1 comma space 6 comma space minus sign 1 close parentheses end cell end table     

Maka, koordinat titik K yang memenuhi adalah open parentheses 1 comma space 6 comma space minus sign 1 close parentheses.

Oleh karena itu, jawaban yang benar adalah B.

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Roboguru

Jarak titik  dengan titik  sama dengan 10. Dengan demikian nilai  ...

Pembahasan Soal:

Rumus jarak titik A equals open parentheses a comma space b comma space c close parentheses dengan B equals left parenthesis d comma space e comma space f right parenthesis adalah :

AB equals square root of open parentheses d bond a close parentheses squared plus open parentheses e bond b close parentheses to the power of 2 end exponent plus open parentheses f bond c close parentheses squared end root 

Dengan menggunakan rumus jarak titik, maka didapatkan :

table attributes columnalign right center left columnspacing 0px end attributes row PQ equals cell square root of left parenthesis minus sign 2 minus sign 6 right parenthesis squared plus left parenthesis 3 minus sign left parenthesis minus sign 3 right parenthesis right parenthesis squared plus left parenthesis 5 minus sign c right parenthesis squared end root end cell row 10 equals cell square root of left parenthesis minus sign 8 right parenthesis squared plus 6 to the power of 2 end exponent plus left parenthesis 5 minus sign c right parenthesis squared end root end cell row cell 10 squared end cell equals cell 64 plus 36 plus left parenthesis 5 minus sign c right parenthesis squared end cell row cell left parenthesis 5 minus sign c right parenthesis squared end cell equals cell 100 minus sign 100 end cell row cell left parenthesis 5 minus sign c right parenthesis squared end cell equals 0 row c equals 5 end table 

Maka, nilai c equals 5.

Oleh karena itu, jawaban yang benar adalah E.

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Roboguru

Jika titik P dan R dalam waktu ditentukan berturut-turut oleh  dan . Jarak P dan R pada saat sama dengan ...

Pembahasan Soal:

Ketika t equals 3, maka titik P :

table attributes columnalign right center left columnspacing 0px end attributes row P equals cell open parentheses table row 4 row cell negative sign italic t minus sign 3 end cell end table close parentheses end cell row blank equals cell open parentheses table row 4 row cell negative sign 3 minus sign 3 end cell end table close parentheses end cell row blank equals cell open parentheses table row 4 row cell negative sign 6 end cell end table close parentheses end cell end table

Titik R :

 table attributes columnalign right center left columnspacing 0px end attributes row R equals cell open parentheses table row cell t squared end cell row cell 2 t end cell end table close parentheses end cell row blank equals cell open parentheses table row cell 3 squared end cell row cell 2 left parenthesis 3 right parenthesis end cell end table close parentheses end cell row blank equals cell open parentheses table row 9 row 6 end table close parentheses end cell end table 

Maka PR :  

table attributes columnalign right center left columnspacing 0px end attributes row cell PR with bar on top end cell equals cell R bond P end cell row blank equals cell open parentheses table row 9 row 6 end table close parentheses minus sign open parentheses table row 4 row cell negative sign 6 end cell end table close parentheses end cell row blank equals cell open parentheses table row cell 9 minus sign 4 end cell row cell 6 minus sign left parenthesis minus sign 6 right parenthesis end cell end table close parentheses end cell row blank equals cell open parentheses table row 5 row 12 end table close parentheses end cell row cell open vertical bar PR with bar on top close vertical bar end cell equals cell square root of 5 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  

Maka, jarak P dan R sama dengan 13.

Oleh karena itu, jawaban yang benar adalah D.

0

Roboguru

O adalah titik awal. Jika  adalah vektor posisi P,  adalah vektor posisi Q dan  adalah vektor posisi R, ;  dan , maka vektor posisi titik U adalah ...

Pembahasan Soal:

Ingatlah bahwa Vektor Posisi adalah vektor yang berpangkal di pusat koordinat straight O open parentheses 0 comma space 0 close parentheses dan berujung di suatu titik misalkan straight A open parentheses straight x comma space straight y close parentheses. Notasi vektor posisi adalah OA with rightwards arrow on top.

Selanjutnya, mIsalkan terdapat dua buah vektor posisi OA with rightwards arrow on top equals straight a with rightwards arrow on top dan OB with rightwards arrow on top equals straight b with rightwards arrow on top. Vektor AB dapat didefinisikan sebagai:

AB with rightwards arrow on top equals OB with rightwards arrow on top minus OA with rightwards arrow on top equals straight b with rightwards arrow on top minus straight a with rightwards arrow on top.

Diketahui vektor posisi:

  • OP with rightwards arrow on top equals straight p with rightwards arrow on top
  • OQ with rightwards arrow on top equals straight q with rightwards arrow on top
  • OR with rightwards arrow on top equals straight r with rightwards arrow on top
  • OS with rightwards arrow on top equals straight s with rightwards arrow on top
  • RS with rightwards arrow on top equals straight q with rightwards arrow on top maka straight s with rightwards arrow on top minus straight r with rightwards arrow on top equals straight q with rightwards arrow on top rightwards arrow straight s with rightwards arrow on top equals straight q with rightwards arrow on top plus straight r with rightwards arrow on top
  • QT with rightwards arrow on top equals straight p with rightwards arrow on top maka straight t with rightwards arrow on top minus straight q with rightwards arrow on top equals straight p with rightwards arrow on top rightwards arrow straight t with rightwards arrow on top equals straight p with rightwards arrow on top plus straight q with rightwards arrow on top
  • SU with rightwards arrow on top equals OT with rightwards arrow on top

Pada soal diketahui SU with rightwards arrow on top equals OT with rightwards arrow on top, maka:

table attributes columnalign right center left columnspacing 0px end attributes row cell SU with rightwards arrow on top end cell equals cell OT with rightwards arrow on top end cell row cell straight u with rightwards arrow on top minus straight s with rightwards arrow on top end cell equals cell straight t with rightwards arrow on top end cell row cell straight u with rightwards arrow on top end cell equals cell straight t with rightwards arrow on top plus straight s with rightwards arrow on top end cell row cell straight u with rightwards arrow on top end cell equals cell straight p with rightwards arrow on top plus straight q with rightwards arrow on top plus straight q with rightwards harpoon with barb upwards on top plus straight r with rightwards harpoon with barb upwards on top end cell row cell straight u with rightwards arrow on top end cell equals cell straight p with rightwards arrow on top plus 2 straight q with rightwards harpoon with barb upwards on top plus straight r with rightwards harpoon with barb upwards on top end cell end table

Dengan demikian, table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell straight u with rightwards arrow on top end cell end table sama dengan table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell straight u with rightwards arrow on top end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell straight p with rightwards arrow on top end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank plus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 2 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell straight q with rightwards harpoon with barb upwards on top end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank plus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell straight r with rightwards harpoon with barb upwards on top end cell end table.

Oleh karena itu, jawaban yang benar adalah D.

0

Roboguru

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

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