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Pertanyaan

Diketahui koordinat titik M ( − 1 , 1 , 6 ) dan N ( − 5 , 5 , − 2 ) . Jika MA : AN = 1 : 3 . Tentukanlah koordinat titik A!

Diketahui koordinat titik  dan . Jika . Tentukanlah koordinat titik A!space

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A. Armanda

Master Teacher

Mahasiswa/Alumni Universitas Indraprasta PGRI

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 straight A open parentheses negative 2 comma space 2 comma space 8 close parentheses.

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Pembahasan

Vektor posisi adalahvektor yang berpangkal di pusat koordinat dan berujung di suatu titik . Nilai vektor posisi akan sama dengan koordinat titik ujungnya. Misalnya, vektor dapat diperoleh dari vektor posisi titik B dikurangi vektor posisi titik A. Diketahuikoordinat titik , , dan . Jadi, .

Vektor posisi adalah vektor yang berpangkal di pusat koordinat open parentheses 0 comma space 0 close parentheses dan berujung di suatu titik open parentheses x comma space y close parentheses.

Nilai vektor posisi akan sama dengan koordinat titik ujungnya.

Misalnya, vektor AB with rightwards arrow on top dapat diperoleh dari vektor posisi titik B dikurangi vektor posisi titik A.

AB with rightwards arrow on top equals b with rightwards arrow on top minus a with rightwards arrow on top 

Diketahui koordinat titik straight M open parentheses negative 1 comma space 1 comma space 6 close parenthesesstraight N open parentheses negative 5 comma space 5 comma space minus 2 close parentheses, dan MA with rightwards arrow on top space colon space AN with rightwards arrow on top equals 1 space colon space 3.

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator MA with rightwards arrow on top space over denominator AN with rightwards arrow on top end fraction end cell equals cell 1 third end cell row cell fraction numerator a with rightwards arrow on top minus m with rightwards arrow on top over denominator n with rightwards arrow on top minus a with rightwards arrow on top end fraction end cell equals cell 1 third end cell row cell 3 open parentheses a with rightwards arrow on top minus m with rightwards arrow on top close parentheses end cell equals cell n with rightwards arrow on top minus a with rightwards arrow on top end cell row cell 3 a with rightwards arrow on top minus 3 m with rightwards arrow on top end cell equals cell n with rightwards arrow on top minus a with rightwards arrow on top end cell row cell 3 a with rightwards arrow on top plus 1 a with rightwards arrow on top end cell equals cell n with rightwards arrow on top plus 3 m with rightwards arrow on top end cell row cell 4 a with rightwards arrow on top end cell equals cell n with rightwards arrow on top plus 3 m with rightwards arrow on top end cell row cell a with rightwards arrow on top end cell equals cell 1 fourth open parentheses n with rightwards arrow on top plus 3 m with rightwards arrow on top close parentheses end cell row cell a with rightwards arrow on top end cell equals cell 1 fourth n with rightwards arrow on top plus 3 over 4 m with rightwards arrow on top end cell row blank equals cell 1 fourth open parentheses table row cell negative 5 end cell row 5 row cell negative 2 end cell end table close parentheses plus 3 over 4 open parentheses table row cell negative 1 end cell row 1 row 6 end table close parentheses end cell row blank equals cell open parentheses table row cell negative 5 over 4 end cell row cell 5 over 4 end cell row cell negative 2 over 4 end cell end table close parentheses plus open parentheses table row cell negative 3 over 4 end cell row cell 3 over 4 end cell row cell fraction numerator 6 times 3 over denominator 4 end fraction end cell end table close parentheses end cell row blank equals cell open parentheses table row cell fraction numerator negative 5 minus 3 over denominator 4 end fraction end cell row cell fraction numerator 5 plus 3 over denominator 4 end fraction end cell row cell fraction numerator negative 2 plus 18 over denominator 2 end fraction end cell end table close parentheses end cell row blank equals cell open parentheses table row cell negative 2 end cell row 2 row 8 end table close parentheses end cell end table 

Jadi, straight A open parentheses negative 2 comma space 2 comma space 8 close parentheses.

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Sharell Earlene Jeoviera

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