document.write( "Question 1064074: ΔABC has vertices at A(8,3), B(7,5), and C(2,4). Point D, located on AC¯ at approximately (6.7,3.22), is the intersection of the altitude drawn from B to AC¯.\r
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\n" ); document.write( "\n" ); document.write( "The area of △ABC is _____ units2.
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Algebra.Com's Answer #679106 by josgarithmetic(39617)\"\" \"About 
You can put this solution on YOUR website!
Segment BD is perpendicular to segment CA. What is the exact intersection point of lines BD and CA? How far is point D from point B?\r
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\n" ); document.write( "\n" ); document.write( "line CA
\n" ); document.write( "\"y-3=%28%284-3%29%282-8%29%29%28x-8%29\"
\n" ); document.write( "\"y-3=-%281%2F6%29%28x-8%29\"
\n" ); document.write( "slope is \"-1%2F6\".\r
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\n" ); document.write( "\n" ); document.write( "line BD
\n" ); document.write( "Need slope to be 6.
\n" ); document.write( "\"y-5=6%28x-7%29\"\r
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\n" ); document.write( "\n" ); document.write( "Now, again, what is the intersection of line CA and BD?
\n" ); document.write( "\"system%28y-3=-%281%2F6%29%28x-8%29%2Cy-5=6%28x-7%29%29\"\r
\n" ); document.write( "\n" ); document.write( "\"system%286y-18=-x%2B8%2Cy=6%28x-7%29%2B5%29\"\r
\n" ); document.write( "\n" ); document.write( "\"system%28x%2B6y=26%2Cy=6x-42%2B5%29\"\r
\n" ); document.write( "\n" ); document.write( "\"system%28x%2B6y=26%2Cy=6x-37%29\"\r
\n" ); document.write( "\n" ); document.write( "\"system%28x%2B6y=26%2C6x-y=37%29\"\r
\n" ); document.write( "\n" ); document.write( "-\r
\n" ); document.write( "\n" ); document.write( "\"x%2B6%286x-37%29=26\"\r
\n" ); document.write( "\n" ); document.write( "\"x%2B36x-6%2A37=26\"\r
\n" ); document.write( "\n" ); document.write( "\"37x=26%2B6%2A37\"\r
\n" ); document.write( "\n" ); document.write( "\"highlight%28x=248%2F37%29\"\r
\n" ); document.write( "\n" ); document.write( "-\r
\n" ); document.write( "\n" ); document.write( "\"y=6%28248%2F37%29-37\"\r
\n" ); document.write( "\n" ); document.write( "\"y=6%2A248%2F37-37%5E2%2F37\"\r
\n" ); document.write( "\n" ); document.write( "\"y=%286%2A248-37%5E2%29%2F37\"\r
\n" ); document.write( "\n" ); document.write( "\"highlight%28y=119%2F37%29\"\r
\n" ); document.write( "\n" ); document.write( "Point D is at \"system%28x=248%2F37%2Cy=119%2F37%29\"\r
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\n" ); document.write( "\n" ); document.write( "What is the distance between D and B? This is the altitude for the base AC.\r
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\n" ); document.write( "\n" ); document.write( "Area for the triangle, \"%281%2F2%29%2AAC%2ABD\"
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