document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=157680>Question 157680</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Show that the points D(-1,-2),E(2,1) and F(-3,6) are the vertices of 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 #116181 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=116181\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let's plot the points first. <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28+300%2C+300%2C+-5%2C+5%2C+-4%2C+7%2Cgrid%28+1+%29%2C%0D%0Acircle%28+-1%2C+-2%2C+.2+%29%2C%0D%0Acircle%28+2%2C+1%2C+.2+%29%2C%0D%0Acircle%28+-3%2C+6%2C+.2+%29%2C%0D%0Agreen%28line%28+-1%2C-2%2C+2%2C+1%29%29%2C%0D%0Agreen%28line%28+2%2C1%2C-3%2C6%29%29%2C%0D%0Agreen%28line%28+-3%2C6%2C+-1%2C+-2%29%29%2C%0D%0Alocate%28-1.5%2C-2%2CD%29%2C%0D%0Alocate%282.2%2C1%2CE%29%2C%0D%0Alocate%28-3.5%2C6%2CF%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "It looks like a right triangle. <BR>\n" );
document.write( "If the triangle is a right triangle, then the sum of the squares of the legs (DE and EF) equals the square of the hypotenuse (DF). <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=DF%5E2=DE%5E2%2BEF%5E2 ALIGN=MIDDLE  ALT=\"DF%5E2=DE%5E2%2BEF%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Let's calculate the lengths of each side and test it.<BR>\n" );
document.write( "The distance formula is <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( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=EF%5E2=%282-%28-3%29%29%5E2%2B%281-6%29%5E2 ALIGN=MIDDLE  ALT=\"EF%5E2=%282-%28-3%29%29%5E2%2B%281-6%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=EF%5E2=%285%29%5E2%2B%28-5%29%5E2 ALIGN=MIDDLE  ALT=\"EF%5E2=%285%29%5E2%2B%28-5%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=EF%5E2=25%2B25 ALIGN=MIDDLE  ALT=\"EF%5E2=25%2B25\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=EF%5E2=50 ALIGN=MIDDLE  ALT=\"EF%5E2=50\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=DE%5E2=%28-1-2%29%5E2%2B%28-2-1%29%5E2 ALIGN=MIDDLE  ALT=\"DE%5E2=%28-1-2%29%5E2%2B%28-2-1%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=DE%5E2=%283%29%5E2%2B%28-3%29%5E2 ALIGN=MIDDLE  ALT=\"DE%5E2=%283%29%5E2%2B%28-3%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=DE%5E2=9%2B9 ALIGN=MIDDLE  ALT=\"DE%5E2=9%2B9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=DE%5E2=18 ALIGN=MIDDLE  ALT=\"DE%5E2=18\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=DF%5E2=%28-1-%28-3%29%29%5E2%2B%28-2-6%29%5E2 ALIGN=MIDDLE  ALT=\"DF%5E2=%28-1-%28-3%29%29%5E2%2B%28-2-6%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=DF%5E2=%282%29%5E2%2B%28-8%29%5E2 ALIGN=MIDDLE  ALT=\"DF%5E2=%282%29%5E2%2B%28-8%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=DF%5E2=4%2B64 ALIGN=MIDDLE  ALT=\"DF%5E2=4%2B64\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=DF%5E2=68 ALIGN=MIDDLE  ALT=\"DF%5E2=68\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=DF%5E2=DE%5E2%2BEF%5E2 ALIGN=MIDDLE  ALT=\"DF%5E2=DE%5E2%2BEF%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=68=18%2B50 ALIGN=MIDDLE  ALT=\"68=18%2B50\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=68=68 ALIGN=MIDDLE  ALT=\"68=68\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "True, therefore the triangle is a right triangle.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );