document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=981367>Question 981367</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Show in two ways that the points (6,1), (2-3), and (4-5) are the vertices of a right Triangle .\r<BR>\n" );
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document.write( "//help me please . Thanks :) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #602364 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=602364\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You meant (6,1), (2,-3), and (4,-5), which indeed are the vertices of a right triangle.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C300%2C-2%2C8%2C-7%2C3%2C%0D%0Agrid%281%29%2C%0D%0Atriangle%286%2C1%2C2%2C-3%2C4%2C-5%29%2C%0D%0Alocate%286.1%2C1.5%2CA%286%2C1%29%29%2C%0D%0Alocate%284%2C-5%2CB%284.1%2C-5%29%29%2C%0D%0Alocate%280.1%2C-2.5%2CC%282%2C-3%29%29%2C%0D%0Alocate%283.1%2C-3.5%2Ca%29%2C%0D%0Alocate%283.5%2C-1.5%2Cb%29%2C%0D%0Alocate%284.5%2C-2%2Cc%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "ONE WAY:<BR>\n" );
document.write( "Show that the line connecting (6,1) and (2,-3) has a slope of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "Show that the line connecting (4,-5) and (2,-3) has a slope of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1 ALIGN=MIDDLE  ALT=\"-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "Since the product of the slopes is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%29%28-1%29=-1 ALIGN=MIDDLE  ALT=\"%281%29%28-1%29=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > , the lines are perpendicular,<BR>\n" );
document.write( "so the triangle has a right angle at (2,-3).<BR>\n" );
document.write( "The slope the line connecting <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%286%2C1%29 ALIGN=MIDDLE  ALT=\"A%286%2C1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%282%2C-3%29 ALIGN=MIDDLE  ALT=\"C%282%2C-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281-%28-3%29%29%2F%286-2%29+=%281%2B3%29%2F4=4%2F4=1 ALIGN=MIDDLE  ALT=\"%281-%28-3%29%29%2F%286-2%29+=%281%2B3%29%2F4=4%2F4=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The slope the line connecting <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B%284%2C-5%29 ALIGN=MIDDLE  ALT=\"B%284%2C-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%282%2C-3%29 ALIGN=MIDDLE  ALT=\"C%282%2C-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-5-%28-3%29%29%2F%284-2%29+=%28-5%2B3%29%2F2=-2%2F2=-1 ALIGN=MIDDLE  ALT=\"%28-5-%28-3%29%29%2F%284-2%29+=%28-5%2B3%29%2F2=-2%2F2=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "ANOTHER WAY:<BR>\n" );
document.write( "Show that the lengths of the sides satisfy the Pythagorean theorem:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c%5E2=a%5E2%2Bb%5E2 ALIGN=MIDDLE  ALT=\"c%5E2=a%5E2%2Bb%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c%5E2=%286-4%29%5E2%2B%281-%28-5%29%29%5E2=2%5E2%2B6%5E2=4%2B36=40 ALIGN=MIDDLE  ALT=\"c%5E2=%286-4%29%5E2%2B%281-%28-5%29%29%5E2=2%5E2%2B6%5E2=4%2B36=40\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2=%282-4%29%5E2%2B%28-3-%28-5%29%29%5E2=%28-2%29%5E2%2B2%5E2=4%2B4=8 ALIGN=MIDDLE  ALT=\"a%5E2=%282-4%29%5E2%2B%28-3-%28-5%29%29%5E2=%28-2%29%5E2%2B2%5E2=4%2B4=8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2=%286-2%29%5E2%2B%281-%28-3%29%29%5E2=4%5E2%2B4%5E2=16%2B16=32 ALIGN=MIDDLE  ALT=\"b%5E2=%286-2%29%5E2%2B%281-%28-3%29%29%5E2=4%5E2%2B4%5E2=16%2B16=32\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " </SPAN>\n" );
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