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Jika  maka segitiga POQ ... (Buat gambar segitiga ...

Jika O left parenthesis 0 comma 0 right parenthesis comma space P left parenthesis 0.2 right parenthesis comma space Q left parenthesis 4 comma 8 right parenthesis maka segitiga POQ ...
(Buat gambar segitiga pada kordinat cartesius, kemudian cari panjang setiap sisi segitiga dengan rumus panjang vector, kemudian pilih option yang paling tepat mewakili hasil perhitungan kalian)

  1. Sama sisispace 

  2. Siku-siku tidak sama kakispace 

  3. Sama kaki tapi tidak siku-sikuspace

  4. Siku-siku dan sama kakispace 

  5. Tidak siku-siku dan tidak sama kakispace

Jawaban:

PQ with rightwards harpoon with barb upwards on top dan open vertical bar PQ with rightwards harpoon with barb upwards on top close vertical bar dapat ditentukan dengan cara berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell P Q end cell equals cell q with rightwards arrow on top minus p with rightwards arrow on top end cell row blank equals cell open parentheses 4 comma 8 close parentheses minus open parentheses 0 comma 2 close parentheses end cell row blank equals cell open parentheses 4 comma 6 close parentheses end cell end table 

table attributes columnalign right center left columnspacing 0px end attributes row cell open vertical bar stack P Q with rightwards arrow on top close vertical bar end cell equals cell square root of 4 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 42 end cell end table 

stack O Q with rightwards arrow on top dan open vertical bar stack O Q with rightwards arrow on top close vertical bar dapat ditentukan dengan cara berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell OQ with rightwards arrow on top end cell equals cell straight o with rightwards arrow on top minus straight p with rightwards arrow on top end cell row blank equals cell open parentheses 0 comma 0 close parentheses minus open parentheses 4 comma 8 close parentheses end cell row blank equals cell open parentheses negative 4 comma negative 8 close parentheses end cell end table  

table attributes columnalign right center left columnspacing 0px end attributes row cell open vertical bar OQ with rightwards arrow on top close vertical bar end cell equals cell square root of open parentheses negative 4 close parentheses squared plus open parentheses negative 8 close parentheses squared end root end cell row blank equals cell square root of 16 plus 64 end root end cell row blank equals cell square root of 80 end cell end table  

OP with rightwards arrow on top dan open vertical bar OP with rightwards arrow on top close vertical bar sebagai berikut

table attributes columnalign right center left columnspacing 0px end attributes row cell OP with rightwards arrow on top end cell equals cell straight p with rightwards arrow on top minus straight o with rightwards arrow on top end cell row blank equals cell open parentheses 0 comma 2 close parentheses minus open parentheses 0 comma 0 close parentheses end cell row blank equals cell open parentheses 0 comma 2 close parentheses end cell end table 

table attributes columnalign right center left columnspacing 0px end attributes row cell open vertical bar stack O P with rightwards arrow on top close vertical bar end cell equals cell square root of 0 squared plus 2 squared end root end cell row blank equals cell square root of 4 end cell row blank equals 2 end table 

Besar sudut POQ

table attributes columnalign right center left columnspacing 0px end attributes row cell cos space theta end cell equals cell fraction numerator stack P O with rightwards arrow on top times stack O Q with rightwards arrow on top over denominator open vertical bar stack P O with rightwards arrow on top close vertical bar open vertical bar stack O Q with rightwards arrow on top close vertical bar end fraction end cell row blank equals cell fraction numerator open parentheses 0 comma 2 close parentheses open parentheses negative 4 comma negative 8 close parentheses over denominator 2 square root of 80 end fraction end cell row blank equals cell fraction numerator negative 16 over denominator 8 square root of 5 end fraction end cell row blank equals cell negative 2 over 5 square root of 5 end cell end table 

Besar sudut PQO

table attributes columnalign right center left columnspacing 0px end attributes row cell cos space alpha end cell equals cell fraction numerator stack P Q with rightwards arrow on top times stack Q O with rightwards arrow on top over denominator open vertical bar stack P Q with rightwards arrow on top close vertical bar open vertical bar stack Q O with rightwards arrow on top close vertical bar end fraction end cell row blank equals cell fraction numerator open parentheses 4 comma 6 close parentheses open parentheses negative 4 comma negative 8 close parentheses over denominator square root of 42 square root of 80 end fraction end cell row blank equals cell fraction numerator negative 16 minus 48 over denominator 4 square root of 210 end fraction end cell row blank equals cell fraction numerator negative 16 over denominator 210 end fraction square root of 210 end cell end table  

Besar cos sudut OPQ

table attributes columnalign right center left columnspacing 0px end attributes row cell cos space beta end cell equals cell fraction numerator stack O P with rightwards arrow on top times stack P Q with rightwards arrow on top over denominator open vertical bar stack O P with rightwards arrow on top close vertical bar open vertical bar stack P Q with rightwards arrow on top close vertical bar end fraction end cell row blank equals cell fraction numerator open parentheses 0 comma 2 close parentheses open parentheses 4 comma 6 close parentheses over denominator 2 square root of 42 end fraction end cell row blank equals cell fraction numerator 0 minus 12 over denominator 2 square root of 42 end fraction end cell row blank equals cell fraction numerator negative 6 over denominator 42 end fraction square root of 42 end cell row blank equals cell negative 1 over 7 square root of 42 end cell end table

Berdasarkan perhitungan panjang ketiga vektor tersebut tidak sama panjang dan sudutnya tidak ada yang siku-siku, maka segitiga tersebut tidak sama kaki. dan tidak siku-siku

Jadi, jawaban yang tepat adalah E

 

 

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