document.write( "Question 632394: The points A (1,5) B (4, -1) & C (-2, -4) forms triangle ABC. Prove that the triangle is right angle and find its area \n" ); document.write( "

Algebra.Com's Answer #398256 by reviewermath(1029) $\"\"$ $\"About$

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a = distance between B and C = $\"sqrt%28%28-4-%28-1%29%29%5E2+%2B+%28-2-4%29%5E2%29+=+sqrt%2845%29+\"$
\n" ); document.write( "b = distance between A and C = $\"sqrt%28%28-4-5%29%5E2+%2B+%28-2-1%29%5E2%29+=+sqrt%2890%29\"$
\n" ); document.write( "c = distance between A and B = $\"sqrt%28%28-1-5%29%5E2+%2B+%284-1%29%5E2%29+=+sqrt%2845%29\"$ \r
\n" ); document.write( "\n" ); document.write( "Therefore $\"a%5E2+%2B+c%5E2+=+b%5E2\"$ because $\"%28sqrt%2845%29%29%5E2+%2B+%28sqrt%2845%29%29%5E2+=+%28sqrt%2890%29%29%5E2\"$ .\r
\n" ); document.write( "\n" ); document.write( "The sides satisfy the Pythagorean Theorem, therefore triangle ABC is a right triangle with angle B as a right angle.\r
\n" ); document.write( "\n" ); document.write( "the area is equal to
\n" ); document.write( " $\"A+=+%28base%29%28height%29%2F2\"$
\n" ); document.write( " $\"A+=+%28sqrt%2845%29%29%28sqrt%2845%29%29%2F2\"$
\n" ); document.write( " $\"highlight%28A+=+22.5%29\"$ square units \n" ); document.write( "

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