document.write( "Question 332266: Triangle ABC has vertices A (-5, 4), B (1, -2) and C (3, 6),
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Algebra.Com's Answer #238152 by Edwin McCravy(20086)\"\" \"About 
You can put this solution on YOUR website!

\n" ); document.write( "Triangle ABC has vertices A (-5, 4), B (1, -2) and C (3, 6),
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document.write( "That triangle is:\r\n" );
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\n" ); document.write( "(a)Write the equation of the line of which AB is a segment.
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document.write( "That's the green line below:\r\n" );
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document.write( "\"y-y%5B1%5D=m%28x-x%5B1%5D%29\"\r\n" );
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document.write( "\"y-%284%29=%28-1%29%28x-%28-5%29%29\"\r\n" );
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document.write( "\"y-4=-%28x%2B5%29\"\r\n" );
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document.write( "\"y-4=-x-5\"\r\n" );
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document.write( "\"y=-x-1\"\r\n" );
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\n" ); document.write( "(b)Write the equation of the line of which the altitude to line AC is a segment.
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document.write( "That's the blue line below:\r\n" );
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document.write( "Since it is an altitude, it is perpendicular to AC.\r\n" );
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document.write( "First we find the slope of AC:\r\n" );
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document.write( "The blue line is perpendicular to AC so its slope is\r\n" );
document.write( "the reciprocal of \"1%2F4\" with the opposite sign, so the\r\n" );
document.write( "blue line's slope is \"-4\" and it passes through B(1,-2)\r\n" );
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document.write( "\"y-y%5B1%5D=m%28x-x%5B1%5D%29\"\r\n" );
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document.write( "\"y-%28-2%29=%28-4%29%28x-%281%29%29\"\r\n" );
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document.write( "\"y%2B2=-4%28x-1%29\"\r\n" );
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document.write( "\"y%2B2=-4x%2B4\"\r\n" );
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document.write( "\"y=-4x%2B2\"\r\n" );
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\n" ); document.write( "(c) Write the equation of the perpendicular bisector of line AC.
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document.write( "We find the midpoint of AC, using the midpoint formula:\r\n" );
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document.write( "Midpoint = (\"%28x%5B1%5D%2Bx%5B2%5D%29%2F2\",\"%28y%5B1%5D%2By%5B2%5D%29%2F2+%29\") = (\"%28%28-5%29%2B%283%29%29%2F2\",\"%284%2B6%29%2F2+%29\") = (\"%28-2%29%2F2\",\"%2810%29%2F2+%29\") = M(-1,5)\r\n" );
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document.write( "Now we find the equation of the red line through M(-1,5), it has the same \r\n" );
document.write( "slope as the altitude since both are perpendicular to the line AC.\r\n" );
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document.write( "The red line's slope is also \"-4\" but it passes through M(-1,5)\r\n" );
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document.write( "\"y-y%5B1%5D=m%28x-x%5B1%5D%29\"\r\n" );
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document.write( "\"y-%285%29=%28-4%29%28x-%28-1%29%29\"\r\n" );
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document.write( "\"y-5=-4%28x%2B1%29\"\r\n" );
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document.write( "\"y-5=-4x-4\"\r\n" );
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document.write( "\"y=-4x%2B1\"\r\n" );
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\n" ); document.write( "(d)Find the perimeter of triangle ABC.
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document.write( "We use the distance formula to find the lengths of all three sides.\r\n" );
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document.write( "\"d=sqrt%28%28x%5B2%5D-x%5B1%5D%29%5E2%2B%28y%5B2%5D-y%5B1%5D%29%5E2%29\"\r\n" );
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document.write( "So the perimeter = AB + BC + AC = \"6sqrt%282%29%2B2sqrt%2817%29%2B2sqrt%2817%29=6sqrt%282%29%2B+4sqrt%2817%29\"\r\n" );
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document.write( "Edwin
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