document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1088408>Question 1088408</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Determine weather triangle QRS is a right triangle for the given vertices.  Explain Q(18,13) R(17,-3) S(-18,12)<BR>\n" );
document.write( " select one:<BR>\n" );
document.write( "a. a. no; QR = sqrt(257), QS = sqrt(1297), RS = sqrt(558) QR2+QS2&#8800; RS2<BR>\n" );
document.write( "b. yes; QR = sqrt(257), QS = sqrt(1297), RS = sqrt(558) RS2+QS2= RQ2<BR>\n" );
document.write( "c. yes; QR = sqrt(257), QS = sqrt(1297), RS = sqrt(558) QR2+QS2&#8800; RS2<BR>\n" );
document.write( "d. no; QR = sqrt(257), QS = sqrt(1297), RS = sqrt(558) RS2+QS2&#8800; RQ2 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #702677 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=702677\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Determine weather triangle QRS is a right triangle for the given vertices. Explain Q(18,13) R(17,-3) S(-18,12)\r<BR>\n" );
document.write( "\n" );
document.write( "sketch triangle first:\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28+600%2C+600%2C+-25%2C+25%2C+-25%2C25%2C%0D%0Acircle%2818%2C13%2C.12%29%2Ccircle%2817%2C-3%2C.12%29%2Ccircle%28-18%2C12%2C.12%29%2C%0D%0Alocate%2818%2C13%2CQ%2818%2C13%29%29%2Clocate%2817%2C-3%2CR%2817%2C-3%29%29%2Clocate%28-18%2C12%2CS%28-18%2C12%29%29%2C%0D%0A%0D%0Agreen%28line%2818%2C13%2C17%2C-3%29%29%2Cgreen%28line%2817%2C-3%2C-18%2C12%29%29%2Cgreen%28line%2818%2C13%2C-18%2C12%29%29%2C%0D%0A+graph%28+600%2C+600%2C+-25%2C+25%2C+-25%2C25%2C+0%29%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=RS ALIGN=MIDDLE  ALT=\"RS\"   DISABLED_style= \"max-width:90%; height:auto;\" > is hypotenuse if triangle QRS  is a right triangle\r<BR>\n" );
document.write( "\n" );
document.write( "find the length: S(-18,12) to R(17,-3)\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=RS=sqrt%28%28-18-17%29%5E2%2B%2812-%28-3%29%29%5E2%29 ALIGN=MIDDLE  ALT=\"RS=sqrt%28%28-18-17%29%5E2%2B%2812-%28-3%29%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=RS=sqrt%28%28-35%29%5E2%2B15%5E2%29 ALIGN=MIDDLE  ALT=\"RS=sqrt%28%28-35%29%5E2%2B15%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=RS=sqrt%281450%29 ALIGN=MIDDLE  ALT=\"RS=sqrt%281450%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=RS=sqrt%2825%2A58%29 ALIGN=MIDDLE  ALT=\"RS=sqrt%2825%2A58%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=RS=5sqrt%2858%29 ALIGN=MIDDLE  ALT=\"RS=5sqrt%2858%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "legs should be: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=QR ALIGN=MIDDLE  ALT=\"QR\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=QS ALIGN=MIDDLE  ALT=\"QS\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "Q(18,13) to R(17,-3)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=QR=sqrt%28%2818-17%29%5E2%2B%2813-%28-3%29%29%5E2%29 ALIGN=MIDDLE  ALT=\"QR=sqrt%28%2818-17%29%5E2%2B%2813-%28-3%29%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=QR=sqrt%281%5E2%2B%2813%2B3%29%5E2%29 ALIGN=MIDDLE  ALT=\"QR=sqrt%281%5E2%2B%2813%2B3%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=QR=sqrt%281%2B16%5E2%29 ALIGN=MIDDLE  ALT=\"QR=sqrt%281%2B16%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=QR=sqrt%28257%29 ALIGN=MIDDLE  ALT=\"QR=sqrt%28257%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "Q(18,13) to S(-18,12)\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=QS=sqrt%28%2818-%28-18%29%29%5E2%2B%2813-12%29%5E2%29 ALIGN=MIDDLE  ALT=\"QS=sqrt%28%2818-%28-18%29%29%5E2%2B%2813-12%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=QS=sqrt%28%2818%2B18%29%5E2%2B%281%29%5E2%29 ALIGN=MIDDLE  ALT=\"QS=sqrt%28%2818%2B18%29%5E2%2B%281%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=QS=sqrt%2836%5E2%2B1%29 ALIGN=MIDDLE  ALT=\"QS=sqrt%2836%5E2%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=QS=sqrt%281296%2B1%29 ALIGN=MIDDLE  ALT=\"QS=sqrt%281296%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=QS=sqrt%281297%29 ALIGN=MIDDLE  ALT=\"QS=sqrt%281297%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "check if: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28SR%29%5E2=%28QR%29%5E2%2B%28QS%29%5E2 ALIGN=MIDDLE  ALT=\"%28SR%29%5E2=%28QR%29%5E2%2B%28QS%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285sqrt%2858%29%29%5E2=%28sqrt%28257%29%29%5E2%2B%28sqrt%281297%29%29%5E2 ALIGN=MIDDLE  ALT=\"%285sqrt%2858%29%29%5E2=%28sqrt%28257%29%29%5E2%2B%28sqrt%281297%29%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1450=257%2B1297 ALIGN=MIDDLE  ALT=\"1450=257%2B1297\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1450%3C%3E1554 ALIGN=MIDDLE  ALT=\"1450%3C%3E1554\"   DISABLED_style= \"max-width:90%; height:auto;\" >=> proves that triangle QRS  is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=not ALIGN=MIDDLE  ALT=\"not\"   DISABLED_style= \"max-width:90%; height:auto;\" > a right triangle\r<BR>\n" );
document.write( "\n" );
document.write( "because <BR>\n" );
document.write( "a.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=QR=sqrt%28257%29 ALIGN=MIDDLE  ALT=\"QR=sqrt%28257%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=QS=sqrt%281297%29 ALIGN=MIDDLE  ALT=\"QS=sqrt%281297%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=RS=5sqrt%2858%29 ALIGN=MIDDLE  ALT=\"RS=5sqrt%2858%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28SR%29%5E2%3C%3E%28QR%29%5E2%2B%28QS%29%5E2 ALIGN=MIDDLE  ALT=\"%28SR%29%5E2%3C%3E%28QR%29%5E2%2B%28QS%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );