document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1052098>Question 1052098</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please Help Me!\r<BR>\n" );
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document.write( "I have a solution that I have been diligently working on but cannot come up with a solution! It is due on the 11 of October and I am in grave need of assistance!\r<BR>\n" );
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document.write( "Problem: A 1-meter wide border must be placed around the triangle in the given picture. Find the equations of the three lines that define the outer edge of this border.\r<BR>\n" );
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document.write( "Picture of problem and video (for hint) is Here:\r<BR>\n" );
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document.write( "Picture link: https://www.scribd.com/document/327019766/Challenge-Problem-2\r<BR>\n" );
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document.write( "Video link (hint): http://screencast.com/t/1f75AMBDW<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #667520 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39617)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=667520\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Equations of the two legs  (because that is a Right Triangle)  is easy.  The tougher part is the equation of the line containing the  the segment 1 meter from the hypotenuse.  \r<BR>\n" );
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document.write( "You have two points on the given triangle's hypotenuse, its endpoints.<BR>\n" );
document.write( "(3,4) and (7,2).  You want to know, what is the equation of the line parallel to the line containing those two points, and is 1 meter away from the line containing those two points?\r<BR>\n" );
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document.write( "Hypotenuse for the given triangle is on the line, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-4=-%28%287-3%29%2F%282-4%29%29%28x-3%29 ALIGN=MIDDLE  ALT=\"y-4=-%28%287-3%29%2F%282-4%29%29%28x-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >;  this is in point slope form, and notice as arranged, the slope is the negative reciprocal of the slope of the line containing the given line's hypotenuse.  Exactly ONE point was picked; that of one of the hypotenuse's endpoints.<BR>\n" );
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document.write( "continuing simplifying the equation<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-4=-%284%2F%28-2%29%29%28x-3%29 ALIGN=MIDDLE  ALT=\"y-4=-%284%2F%28-2%29%29%28x-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-4=2%28x-3%29 ALIGN=MIDDLE  ALT=\"y-4=2%28x-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=2x-6%2B4 ALIGN=MIDDLE  ALT=\"y=2x-6%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%28y=2x-2%29 ALIGN=MIDDLE  ALT=\"highlight_green%28y=2x-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
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document.write( "Note that this line, y=2x-2, is PERPENDICULAR to the hypotenuse of the given traingle shown in your graph as given.\r<BR>\n" );
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document.write( "Next question to solve on your way to your exercise's question:<BR>\n" );
document.write( "What is the ordered pair for the point 1 meter away from point (3,4) and on the line  y=2x-2 ?<BR>\n" );
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document.write( "Use the Distance Formula and the unknown ordered pair   ( x, 2x-2 ).<BR>\n" );
document.write( "To fill the distance formula for this stage of the solution will look like this...<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28%28x-3%29%5E2%2B%28%282x-2%29-4%29%5E2%29=1 ALIGN=MIDDLE  ALT=\"sqrt%28%28x-3%29%5E2%2B%28%282x-2%29-4%29%5E2%29=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and understand, you will get probably two answers for this x, and you will need to decide which to accept and which to reject.<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-3%29%5E2%2B%282x-6%29%5E2=1 ALIGN=MIDDLE  ALT=\"%28x-3%29%5E2%2B%282x-6%29%5E2=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-6x%2B9%2B4x%5E2-24x%2B36=1 ALIGN=MIDDLE  ALT=\"x%5E2-6x%2B9%2B4x%5E2-24x%2B36=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x%5E2-30x%2B45=1 ALIGN=MIDDLE  ALT=\"5x%5E2-30x%2B45=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x%5E2-30x%2B44=0 ALIGN=MIDDLE  ALT=\"5x%5E2-30x%2B44=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Discriminant, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28900-4%2A5%2A44%29=900-20%2A44=900-880=20 ALIGN=MIDDLE  ALT=\"%28900-4%2A5%2A44%29=900-20%2A44=900-880=20\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "which is  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2A2%2A5%2A2%2A5=2%5E3%2A5%5E2 ALIGN=MIDDLE  ALT=\"2%2A2%2A5%2A2%2A5=2%5E3%2A5%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%2830%2B-+sqrt%282%5E2%2A5%5E2%2A2%29%29%2F%282%2A5%29 ALIGN=MIDDLE  ALT=\"x=%2830%2B-+sqrt%282%5E2%2A5%5E2%2A2%29%29%2F%282%2A5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%2830%2B-+10%2Asqrt%282%29%29%2F10 ALIGN=MIDDLE  ALT=\"x=%2830%2B-+10%2Asqrt%282%29%29%2F10\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=3%2B-+sqrt%282%29 ALIGN=MIDDLE  ALT=\"x=3%2B-+sqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >-------------To best know which of these will work for the problem, find each corresponding y-coordinate for this x.\r<BR>\n" );
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document.write( "The MINUS form using 2x-2, becomes <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%283-sqrt%282%29%29-2=6-2-2sqrt%282%29-2=4-2%2Asqrt%282%29 ALIGN=MIDDLE  ALT=\"2%283-sqrt%282%29%29-2=6-2-2sqrt%282%29-2=4-2%2Asqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "The PLUS form gives for y,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%283%2Bsqrt%282%29%29-2 ALIGN=MIDDLE  ALT=\"2%283%2Bsqrt%282%29%29-2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2B2sqrt%282%29-2 ALIGN=MIDDLE  ALT=\"6%2B2sqrt%282%29-2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2B2sqrt%282%29 ALIGN=MIDDLE  ALT=\"4%2B2sqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The PLUS form result is probably the point you need.<BR>\n" );
document.write( "Ordered pair for the point 1 meter from given triangle's hypotenuse would be  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28x=3%2Bsqrt%282%29%2Cy=4%2B2sqrt%282%29%29 ALIGN=MIDDLE  ALT=\"system%28x=3%2Bsqrt%282%29%2Cy=4%2B2sqrt%282%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "FINAL QUESTION:<BR>\n" );
document.write( "Equation for the line containing point   <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28x=3%2Bsqrt%282%29%2Cy=4%2B2sqrt%282%29%29 ALIGN=MIDDLE  ALT=\"system%28x=3%2Bsqrt%282%29%2Cy=4%2B2sqrt%282%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and having slope 2.<BR>\n" );
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document.write( "You might want to start this in the point-slope form,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28y-%284%2B2sqrt%282%29%29=2%28x-%283%2Bsqrt%282%29%29%29%29 ALIGN=MIDDLE  ALT=\"highlight%28y-%284%2B2sqrt%282%29%29=2%28x-%283%2Bsqrt%282%29%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and you can simplify this in whatever way you need or want. </SPAN>\n" );
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