document.write( "Question 421448: Determine whether the given coordinates are the vertices of a triangle. Explain.
\n" ); document.write( "problem #1. S(6,5), T(8,3), U(12,-1)
\n" ); document.write( "problem #2. D(1,-5), E(-3,0), F(-1,0) \n" ); document.write( "
Algebra.Com's Answer #330350 by cleomenius(959)\"\" \"About 
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Using the distance formula, \"sqrt%28%28x2+-x1%29%5E2+%2B+%28y2+-+y1%29%5E2+%29\"
\n" ); document.write( "I determined the distance between the points.
\n" ); document.write( "st = 2.8242
\n" ); document.write( "ut = 5.6568
\n" ); document.write( "su = 8.4852\r
\n" ); document.write( "\n" ); document.write( "By the triangle inequality thereom, the sum of any two sides of a triangle is > than the length of the third side.\r
\n" ); document.write( "\n" ); document.write( "adding st and ut, the result is < su. This would not fit the criteria for the vertexes of a triangle.\r
\n" ); document.write( "\n" ); document.write( "For the second set,\r
\n" ); document.write( "\n" ); document.write( "de = 6.4
\n" ); document.write( "ef = 4.0
\n" ); document.write( "fd = 5.4\r
\n" ); document.write( "\n" ); document.write( "This example does satisfy the triangle inequality thereom, it will be a valid triangle.\r
\n" ); document.write( "\n" ); document.write( "Cleomenius.
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