document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=135147>Question 135147</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Prove that the triangle with vertices(13,-1),(-9,3),(-3,-9) is a right triangle. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #99084 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><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=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=99084\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let's name the points<BR>\n" );
document.write( "A (13,-1)<BR>\n" );
document.write( "B (-9,3)<BR>\n" );
document.write( "C (-3,-9)<BR>\n" );
document.write( "For a right triangle the sums of the squares of the two legs equal the square of the hypotenuse, the longest leg.<BR>\n" );
document.write( "Calculate each leg length first using the distance formula between two points.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D%5E2=%28x%5B1%5D-x%5B2%5D%29%5E2%2B%28y%5B1%5D-y%5B2%5D%29%5E2 ALIGN=MIDDLE  ALT=\"D%5E2=%28x%5B1%5D-x%5B2%5D%29%5E2%2B%28y%5B1%5D-y%5B2%5D%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "AB, the distance from point A to point B. <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28AB%29%5E2=%2813-%28-9%29%29%5E2%2B%28-1-3%29%5E2 ALIGN=MIDDLE  ALT=\"%28AB%29%5E2=%2813-%28-9%29%29%5E2%2B%28-1-3%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28AB%29%5E2=%2822%29%5E2%2B%284%29%5E2 ALIGN=MIDDLE  ALT=\"%28AB%29%5E2=%2822%29%5E2%2B%284%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28AB%29%5E2=484%2B16 ALIGN=MIDDLE  ALT=\"%28AB%29%5E2=484%2B16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "AC, the distance from point A to point C. <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28AC%29%5E2=%2813-%28-3%29%29%5E2%2B%28-1-%28-9%29%29%5E2 ALIGN=MIDDLE  ALT=\"%28AC%29%5E2=%2813-%28-3%29%29%5E2%2B%28-1-%28-9%29%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28AC%29%5E2=%2816%29%5E2%2B%288%29%5E2 ALIGN=MIDDLE  ALT=\"%28AC%29%5E2=%2816%29%5E2%2B%288%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28AC%29%5E2=256%2B64 ALIGN=MIDDLE  ALT=\"%28AC%29%5E2=256%2B64\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28AC%29%5E2=320 ALIGN=MIDDLE  ALT=\"%28AC%29%5E2=320\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "BC, the distance from point B to point C. <BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28BC%29%5E2=%28-6%29%5E2%2B%2812%29%5E2 ALIGN=MIDDLE  ALT=\"%28BC%29%5E2=%28-6%29%5E2%2B%2812%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28BC%29%5E2=36%2B144 ALIGN=MIDDLE  ALT=\"%28BC%29%5E2=36%2B144\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28BC%29%5E2=180 ALIGN=MIDDLE  ALT=\"%28BC%29%5E2=180\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Since AB is the largest, it is the hypotenuse. <BR>\n" );
document.write( "If it is a right triangle then,<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=500=500 ALIGN=MIDDLE  ALT=\"500=500\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "True statement. <BR>\n" );
document.write( "Those point, therefore, define a right triangle.  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );