Pertanyaan

[SPMB 2004] Diketahui bidang empat ABCD. D A = a , D B = b , D C = c .Jika titik Q pada AB dengan AQ : QB = 1 : 2, dan titik R pada BC dengan BR : RC = 1 : 2 maka QR = ....

[SPMB 2004]
Diketahui bidang empat ABCD. $D A = a, D B = b, D C = c$ . Jika titik Q pada AB dengan AQ : QB = 1 : 2, dan titik R pada BC dengan BR : RC = 1 : 2 maka $QR =$ ....

$fraction numerator negative a with rightwards arrow on top plus b with rightwards arrow on top plus c with rightwards arrow on top over denominator 3 end fraction$
$fraction numerator a with rightwards arrow on top plus b with rightwards arrow on top plus c with rightwards arrow on top over denominator 3 end fraction$
$fraction numerator negative 2 a with rightwards arrow on top plus b with rightwards arrow on top plus c with rightwards arrow on top over denominator 3 end fraction$
$fraction numerator negative 2 a with rightwards arrow on top minus b with rightwards arrow on top minus c with rightwards arrow on top over denominator 3 end fraction$
$fraction numerator negative 2 a with rightwards arrow on top plus b with rightwards arrow on top minus c with rightwards arrow on top over denominator 3 end fraction$

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Pembahasan

Perhatikan bahwa : Lalu perhatikan:

Perhatikan bahwa :
stack D A with rightwards arrow on top plus stack A B with rightwards arrow on top equals stack D B with rightwards arrow on top a with rightwards arrow on top plus stack A B with rightwards arrow on top equals b with rightwards arrow on top stack A B with rightwards arrow on top equals b with rightwards arrow on top minus a with rightwards arrow on top

Lalu perhatikan:
$stack Q R with rightwards arrow on top equals stack Q B with rightwards arrow on top plus stack B R with rightwards arrow on top stack Q R with rightwards arrow on top equals 2 over 3 stack A B with rightwards arrow on top plus 1 third stack B C with rightwards arrow on top stack Q R with rightwards arrow on top equals 2 over 3 open parentheses b with rightwards arrow on top minus a with rightwards arrow on top close parentheses plus 1 third open parentheses stack B D with rightwards arrow on top plus stack D C with rightwards arrow on top close parentheses stack Q R with rightwards arrow on top equals 2 over 3 open parentheses b with rightwards arrow on top minus a with rightwards arrow on top close parentheses plus 1 third open parentheses negative b with rightwards arrow on top plus c with rightwards arrow on top close parentheses stack Q R with rightwards arrow on top equals 2 over 3 b with rightwards arrow on top minus 2 over 3 a with rightwards arrow on top minus 1 third b with rightwards arrow on top plus 1 third c with rightwards arrow on top stack Q R with rightwards arrow on top equals fraction numerator negative 2 a with rightwards arrow on top plus b with rightwards arrow on top plus c with rightwards arrow on top over denominator 3 end fraction$

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