document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=6654>Question 6654</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the value of a if the points whose coordinates are given are the indicated distance apart.<BR>\n" );
document.write( "(-2,-5)(a,7);d=13 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #3638 by </B><A HREF=/tutors/aboutme.mpl?userid=longjonsilver><B>longjonsilver(2297)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=longjonsilver><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=longjonsilver><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=3638\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> this is a reverse version of the typical question of giving 2 points and finding the distance between them.\r<BR>\n" );
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document.write( "It uses Pythagoras' Theorem...\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%287-%28-5%29%29%5E2+%2B+%28a-%28-2%29%29%5E2+=+13%5E2 ALIGN=MIDDLE  ALT=\"%287-%28-5%29%29%5E2+%2B+%28a-%28-2%29%29%5E2+=+13%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%287%2B5%29%5E2+%2B+%28a%2B2%29%5E2+=+13%5E2 ALIGN=MIDDLE  ALT=\"%287%2B5%29%5E2+%2B+%28a%2B2%29%5E2+=+13%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2812%29%5E2+%2B+%28a%2B2%29%5E2+=+13%5E2 ALIGN=MIDDLE  ALT=\"%2812%29%5E2+%2B+%28a%2B2%29%5E2+=+13%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now, if you know anything about Pythagoras' theorm, you should know about a 5, 12, 13 triangle. We have this here...so a+2=5 --> a=3. But doing it this way is dangerous, because we will miss an answer... see below:\r<BR>\n" );
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document.write( "The full proper answer is as follows:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=144+%2B+%28a%2B2%29%5E2+=+169 ALIGN=MIDDLE  ALT=\"144+%2B+%28a%2B2%29%5E2+=+169\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a%2B2%29%5E2+=+169-144 ALIGN=MIDDLE  ALT=\"%28a%2B2%29%5E2+=+169-144\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a%2B2%29%5E2+=+25 ALIGN=MIDDLE  ALT=\"%28a%2B2%29%5E2+=+25\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "so, either <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2B2+=+sqrt%2825%29 ALIGN=MIDDLE  ALT=\"a%2B2+=+sqrt%2825%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2B2+=+-+sqrt%2825%29 ALIGN=MIDDLE  ALT=\"a%2B2+=+-+sqrt%2825%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "ie a+2 = 5 OR a+2 = -5<BR>\n" );
document.write( "so a=3 or a=-7\r<BR>\n" );
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document.write( "so, a line joining point (-2,-5) to either (3,7) or (-7,7) will give a length of 13.\r<BR>\n" );
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document.write( "jon. </SPAN>\n" );
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