document.write( "Question 438202: Decide whether the points are the vertices of a right triangle. (2,0), (-1,-1), (1,3) \n" ); document.write( "

Algebra.Com's Answer #303107 by robertb(5830) $\"\"$ $\"About$

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$\"V%5B1%5D\"$ = <-1-2, -1-0> = <-3, -1>
\n" ); document.write( " $\"V%5B2%5D\"$ = <1--1, 3--1> = <2, 4>
\n" ); document.write( " $\"V%5B3%5D\"$ = <1-2, 3-0> = <-1, 3>\r
\n" ); document.write( "\n" ); document.write( "Take dot products:
\n" ); document.write( " $\"V%5B1%5D%2AV%5B2%5D+=+-6+-+4+=+-10\"$
\n" ); document.write( " $\"V%5B2%5D%2AV%5B3%5D+=+-2+%2B+12+=+10\"$
\n" ); document.write( " $\"V%5B1%5D%2AV%5B3%5D+=+3+-+3+=+0\"$
\n" ); document.write( "==> the sides of the triangle, $\"V%5B1%5D\"$ and $\"V%5B3%5D\"$ are perpendicular, and so the triangle is a right triangle. \n" ); document.write( "

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