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Prove that (2,-2) ,(-2,1) and(5,2) are …

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Prove that (2,-2) ,(-2,1) and(5,2) are the vertices of an right angled triangle .Find the area and hypotenuse

Posted by Saswat Patro 4 years, 7 months ago

CBSE > Class 10 > Mathematics

1 answers

Salil Chandra 4 years, 7 months ago

Proof: By distance formula, AB=(−2−2)2+(1+2)2=16+9=25=5 BC=(−2−5)2+(1−2)2=(−7)2+(−1)2=50=52 Length of the hypotenuse AC=(5−2)2+(2+2)2=(3)2+(4)2=25 ∴AB2+AC2=25+25=50=BC2 ∴ △ ABC is a right-angled triangle Area of the triangle ABC = 21[x1(y2−y3)+x2(y3−y1)+x3(y1−y2)]sq. Area of the △ABC =21×Base×height =21×5×5 =225sq.units.

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