document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=386488>Question 386488</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Use the graphs of y=2x+6, 3x+2y=19 and y=2, which contain the sides of a triangle.\r<BR>\n" );
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document.write( "1. Find the coordinates of the vertices of the triangle.\r<BR>\n" );
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document.write( "2. Find the area of the triangle </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #273225 by </B><A HREF=/tutors/aboutme.mpl?userid=Alan3354><B>Alan3354(69443)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Alan3354><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=Alan3354><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=273225\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Use the graphs of y=2x+6, 3x+2y=19 and y=2, which contain the sides of a triangle. <BR>\n" );
document.write( "1. Find the coordinates of the vertices of the triangle. <BR>\n" );
document.write( "2. Find the area of the triangle<BR>\n" );
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document.write( "I don't know of a \"slick\" or elegant way to do this, just grind it out.<BR>\n" );
document.write( "Sub y=2 into the other eqns to find the vertices.<BR>\n" );
document.write( "y=2x+6 and y=2<BR>\n" );
document.write( "2 = 2x+6<BR>\n" );
document.write( "x = -2 --> (-2,2) vertex A<BR>\n" );
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document.write( "3x+2y=19 and y=2<BR>\n" );
document.write( "3x+4 = 19<BR>\n" );
document.write( "x = 5 --> (5,2) vertex B<BR>\n" );
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document.write( "y=2x+6<BR>\n" );
document.write( "3x+2y=19<BR>\n" );
document.write( "Sub for y<BR>\n" );
document.write( "3x + 2(2x+6) = 19<BR>\n" );
document.write( "7x + 12 = 19<BR>\n" );
document.write( "x = 1 --> (1,8) vertex C<BR>\n" );
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document.write( "To find the area, list the points in columns and repeat the 1st point<BR>\n" );
document.write( "The + signs are for alignment<BR>\n" );
document.write( ".A...B...C...A<BR>\n" );
document.write( "-2 +5 +1 -2<BR>\n" );
document.write( "+2 +2 +8 +2<BR>\n" );
document.write( "Starting at the left, add the products of the upward diagonals, the the downward<BR>\n" );
document.write( "Upward:<BR>\n" );
document.write( "2*5 + 2*1 + 8*-2 = 10 + 2 - 16 = -4<BR>\n" );
document.write( "Downward:<BR>\n" );
document.write( "-2*2 + 5*8 + 1*2 = -4 + 40 + 2 = 38<BR>\n" );
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document.write( "The difference is 38 -(-4) = 42<BR>\n" );
document.write( "The area is 1/2 that, = 21 sq units<BR>\n" );
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document.write( "PS  The method for calculating area works for polygons of any shape, and any number of sides.  It doesn't seem to be well known.<BR>\n" );
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