document.write( "Question 77778This question is from textbook Geometry for Enjoyment and Challenge
\n" ); document.write( ": I need your help with this:\r
\n" ); document.write( "\n" ); document.write( "Write an equation of the altitude from C to line segment AB. The coordinates of C are (4,12), A (2,1), and B (16,3). \n" ); document.write( "
Algebra.Com's Answer #55771 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Write an equation of the altitude from C to line \r\n" );
document.write( "segment AB. The coordinates of C are (4,12), \r\n" );
document.write( "A (2,1), and B (16,3). \r\n" );
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document.write( "Here is the triangle.  \r\n" );
document.write( "A is the lower left vertex where the red line\r\n" );
document.write( "segment AC meets the blue line segment AB.\r\n" );
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document.write( "B is the lower right vertex where the dark blue line\r\n" );
document.write( "segment AB meets the green line sengment BC\r\n" );
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document.write( "C is the upper vertex where the red line\r\n" );
document.write( "segment AC meets the green line segment BC\r\n" );
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document.write( "Now let's draw in the altitude from vertex C \r\n" );
document.write( "(the upper vertex) to the dark blue line segment AB.\r\n" );
document.write( "I'll draw it in light blue.\r\n" );
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document.write( "Let's find the slope of the dark blue line \r\n" );
document.write( "segment AB by using the slope formula:\r\n" );
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document.write( "     y2 - y1\r\n" );
document.write( "m = —————————\r\n" );
document.write( "     x2 - x1\r\n" );
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document.write( "where (x1, y1) = A(2, 1) and (x2, y2) = B(16, 3)\r\n" );
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document.write( "     (3) - (1)      2     1\r\n" );
document.write( "m = ——————————— = ———— = ——— \r\n" );
document.write( "    (16) - (2)     14     7 \r\n" );
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document.write( "An altitude is perpendicular to the side it's drawn to.\r\n" );
document.write( "So the slope of the altitude (light blue line segment) is\r\n" );
document.write( "the reciprocal of 1/7 with the sign changed.  That would\r\n" );
document.write( "be -7/1 or -7.\r\n" );
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document.write( "We know that a point on the altitude (light blue line) is\r\n" );
document.write( "the vertex C(4,12), so we use (x1, y1) = (4, 12)\r\n" );
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document.write( "Now substitute in the point slope formula:\r\n" );
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document.write( "   y - y1 = m(x - x1)\r\n" );
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document.write( "   y - 12 = 7(x - 4)\r\n" );
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document.write( "   y - 12 = 7x - 28\r\n" );
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document.write( "        y = 7x - 16\r\n" );
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document.write( "That's the equation of the blue line segment which\r\n" );
document.write( "is the light blue line.  However, this is the \r\n" );
document.write( "equation of the ENTIRE LINE as we see here, i.e., \r\n" );
document.write( "the EXTENDED altitude, not just the altitude,\r\n" );
document.write( "which is only a line segment, as you see below.\r\n" );
document.write( "I suppose that's what you wanted.\r\n" );
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document.write( "Edwin
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