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Diketahui  dengan titik-titik  dan . Apakah segiti...

Diketahui undefined dengan titik-titik begin mathsize 14px style A open parentheses negative 1 comma 5 close parentheses comma space B open parentheses negative 1 comma 1 close parentheses end style dan begin mathsize 14px style C open parentheses 2 comma 1 close parentheses end style. Apakah segitiga begin mathsize 14px style A B C end style merupakan segitiga siku-siku? Jelaskan. 

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Jawaban:

Segitiga ABC dengan titik-titik begin mathsize 14px style A open parentheses negative 1 comma 5 close parentheses comma space B open parentheses negative 1 comma 1 close parentheses comma space end style dan begin mathsize 14px style C open parentheses 2 comma 1 close parentheses end style 

Panjang sisi-sisi segitiga ABC adalah 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell A B end cell equals cell square root of open parentheses negative 1 minus open parentheses negative 1 close parentheses close parentheses squared plus open parentheses 1 minus 5 close parentheses squared end root end cell row blank equals cell square root of 0 squared plus open parentheses negative 4 close parentheses squared end root end cell row blank equals cell square root of 16 end cell row blank equals 4 end table end style 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell A C end cell equals cell square root of open parentheses 2 minus open parentheses negative 1 close parentheses close parentheses squared plus open parentheses 1 minus 5 close parentheses squared end root end cell row blank equals cell square root of 3 squared plus open parentheses negative 4 close parentheses squared end root end cell row blank equals cell square root of 9 plus 16 end root end cell row blank equals cell square root of 25 end cell row blank equals 5 end table end style 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell B C end cell equals cell square root of open parentheses 2 minus open parentheses negative 1 close parentheses close parentheses squared plus open parentheses 1 minus 1 close parentheses squared end root end cell row blank equals cell square root of 3 squared plus 0 squared end root end cell row blank equals cell square root of 9 end cell row blank equals cell 3 space end cell end table end style 

Perhatikan bahwa 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank blank row cell A B squared plus B C squared end cell equals cell 3 squared plus 4 squared end cell row blank equals cell 9 plus 16 end cell row blank equals 25 row blank equals cell 5 squared end cell row cell A B squared plus B C squared end cell equals cell A C squared end cell end table end style 

Maka berdasarkan teorema Pythagoras segitiga ABC adalah segitiga siku-siku 

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