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Diketahui ∆ABC dengan titik titik A (-1,5) B (-1,1) dan C (2,1) apakah segitiga ABC merupakan segitiga siku-siku? jelaskan.

Pertanyaan

Diketahui ∆ABC dengan titik titik A (-1,5) B (-1,1) dan C (2,1) apakah segitiga ABC merupakan segitiga siku-siku? jelaskan.

Pembahasan Soal:

Untuk sembarang titikbegin mathsize 14px style straight A left parenthesis straight x subscript 1 comma space straight y subscript 1 right parenthesis end style dan begin mathsize 14px style straight B left parenthesis straight x subscript 2 comma space straight y subscript 2 right parenthesis end style, maka panjang AB atau jarak AB = begin mathsize 14px style square root of open parentheses x subscript 2 minus x subscript 1 close parentheses squared plus open parentheses y subscript 2 minus y subscript 1 close parentheses squared end root end style.

begin mathsize 14px style straight A left parenthesis negative 1 comma space 5 right parenthesis end style dan begin mathsize 14px style straight B left parenthesis negative 1 comma space 1 right parenthesis end style 

begin mathsize 14px style straight x subscript 1 equals negative 1 comma space straight y subscript 1 equals 5 straight x subscript 2 equals negative 1 comma space straight y subscript 2 equals 1 end style

begin mathsize 14px style AB equals square root of open parentheses negative 1 minus left parenthesis negative 1 right parenthesis close parentheses squared plus left parenthesis 1 minus 5 right parenthesis squared end root space space space space space equals square root of 0 squared plus left parenthesis negative 4 right parenthesis squared end root space space space space space equals square root of 16 space space space space space equals 4 end style

begin mathsize 14px style straight B left parenthesis negative 1 comma space 1 right parenthesis end style dan begin mathsize 14px style straight C left parenthesis 2 comma space 1 right parenthesis end style

begin mathsize 14px style straight x subscript 1 equals negative 1 comma space straight y subscript 1 equals 1 straight x subscript 2 equals 2 comma space straight y subscript 2 equals 1 end style

begin mathsize 14px style BC equals square root of open parentheses 2 minus left parenthesis negative 1 right parenthesis close parentheses squared plus open parentheses 1 minus 1 close parentheses squared end root space space space space space equals square root of left parenthesis 3 right parenthesis squared plus 0 squared end root space space space space space equals square root of 9 space space space space space equals 3 end style

begin mathsize 14px style straight A left parenthesis negative 1 comma space 5 right parenthesis end style dan begin mathsize 14px style straight C left parenthesis 2 comma space 1 right parenthesis end style

begin mathsize 14px style straight x subscript 1 equals negative 1 comma space straight y subscript 1 equals 5 straight x subscript 2 equals 2 comma space straight y subscript 2 equals 1 end style

begin mathsize 14px style AC equals square root of open parentheses 2 minus left parenthesis negative 1 right parenthesis close parentheses squared plus open parentheses 1 minus 5 close parentheses squared end root space space space space space equals square root of 3 squared plus left parenthesis negative 4 right parenthesis squared end root space space space space space equals square root of 9 plus 16 end root space space space space space equals square root of 25 space space space space space equals 5 end style

Berikut pembuktiannya:

begin mathsize 14px style AB squared plus BC squared equals AC squared left right double arrow 4 squared plus 3 squared equals 5 squared left right double arrow 16 plus 9 equals 25 left right double arrow 25 space equals 25 end style

Jadi Δ ABC merupakan segitiga siku-siku, karena ketiga sisinya merupakan tripel pythagoras.

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 10 Juni 2021

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