document.write( "Question 253715: Determine whether the given coordinates are the vertices of a triangle.\r
\n" ); document.write( "\n" ); document.write( "1. A(3,5), B(4,7), C(7,6)\r
\n" ); document.write( "\n" ); document.write( "2. S(6,5), T(8,3), U(12,-1)\r
\n" ); document.write( "\n" ); document.write( "3. H(-8,4), I(-4,2), J(4,-2)\r
\n" ); document.write( "\n" ); document.write( "4. D(1,-5), E(-3,0), F(-1,0)\r
\n" ); document.write( "\n" ); document.write( "5. R(1,3), S(4,0), T(10,-6)\r
\n" ); document.write( "\n" ); document.write( "6. W(2,6), X(1,6), Y(4,2)\r
\n" ); document.write( "\n" ); document.write( "7. P(-3,2), L(1,1), M(9,-1)\r
\n" ); document.write( "\n" ); document.write( "8. B(1,1), C(6,5), D(4,-1) \n" ); document.write( "

Algebra.Com's Answer #186066 by Edwin McCravy(20056) $\"\"$ $\"About$

You can put this solution on YOUR website!

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document.write( "I'll just do 1 of each type, number 1 and 3.  The others\r\n" );
document.write( "are done exactly like one of those. 1 forms a triangle and 3 doesn't.\r\n" );
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\n" ); document.write( "1. A(3,5), B(4,7), C(7,6)
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document.write( "Yes they do.  How to tell using algebra and without looking at a graph:\r\n" );
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document.write( "Three points either form a triangle or they form a line (said\r\n" );
document.write( "to be \"co-linear\")\r\n" );
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document.write( "You find the slopes of the segments joining any two pairs of the\r\n" );
document.write( "three points.  If they are different, they don't form a straight \r\n" );
document.write( "line, and thus they form a triangle. If they have the same slope \r\n" );
document.write( "they form a straight line, and do not form a triangle.\r\n" );
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document.write( "So we find the slopes of AB and AC. (We could also have found the\r\n" );
document.write( "slope of BC, but it is only necessary to find the slopes of two\r\n" );
document.write( "of the segments:\r\n" );
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document.write( ", \r\n" );
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document.write( "They are not the same so the points do not lie in a straight line, and\r\n" );
document.write( "therefore they form a triangle.\r\n" );
document.write( "

\n" ); document.write( "3. H(-8,4), I(-4,2), J(4,-2)
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document.write( "No they don't. They form a straight line. How to tell using algebra \r\n" );
document.write( "and without looking at a graph:\r\n" );
document.write( "\r\n" );
document.write( "Three points either form a triangle or they form a line (said\r\n" );
document.write( "to be \"co-linear\").  These are co-linear.\r\n" );
document.write( "\r\n" );
document.write( "You find the slopes of the segments joining any two pairs of the\r\n" );
document.write( "three points.  If they are different, they don't form a straight \r\n" );
document.write( "line, and thus they form a triangle. If they have the same slope \r\n" );
document.write( "they form a straight line, and do not form a triangle.\r\n" );
document.write( "\r\n" );
document.write( "So we find the slopes of HI and IJ. (We could also have found the\r\n" );
document.write( "slope of HJ, but it is only necessary to find the slopes of two\r\n" );
document.write( "of the segments:\r\n" );
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document.write( ", \r\n" );
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document.write( "They are the same so the points lie in a straight line, and\r\n" );
document.write( "therefore they do not form a triangle.\r\n" );
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document.write( "All the others are like one of these.  You do the rest of them by\r\n" );
document.write( "yourself.\r\n" );
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document.write( "Edwin

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