document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=177793>Question 177793</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Analytic Geometry<BR>\n" );
document.write( "1.a) Draw the triangle with vertices P(-2,-2), Q(2,4), and R(8,0). <BR>\n" );
document.write( "b) Show algebraically that PQR is a right triangle.<BR>\n" );
document.write( "c) Is PQR also an isosceles triangle?<BR>\n" );
document.write( "Use algebraic reasoning to justify your answer.<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #132787 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=132787\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a.)<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28+300%2C+300%2C+-10%2C+10%2C+-10%2C+10%2Cgrid%28+1+%29%2C%0D%0Acircle%28+-2%2C+-2%2C+.3+%29%2C%0D%0Acircle%28+2%2C+4%2C+.3+%29%2C%0D%0Acircle%28+8%2C+0%2C+.3+%29%2C%0D%0Alocate%28-2.5%2C-1%2CP%29%2C%0D%0Alocate%282.2%2C5.2%2CQ%29%2C%0D%0Alocate%288.2%2C1%2CR%29%2C%0D%0Agreen%28line%28+-2%2C+-2%2C+2%2C+4%29%29%2C%0D%0Agreen%28line%28+2%2C+4%2C+8%2C0%29%29%2C%0D%0Agreen%28line%28+8%2C+0%2C+-2%2C+-2%29%29%0D%0A%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "b.) You can use the Pythagoran theorem to check if PQR is a right triangle.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=PQ%5E2%2BQR%5E2=PR%5E2 ALIGN=MIDDLE  ALT=\"PQ%5E2%2BQR%5E2=PR%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "Using the distance formula to calculate line segment lengths,<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" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=PQ%5E2=%28-2-2%29%5E2%2B%28-2-4%29%5E2 ALIGN=MIDDLE  ALT=\"PQ%5E2=%28-2-2%29%5E2%2B%28-2-4%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=PQ%5E2=%28-4%29%5E2%2B%28-6%29%5E2 ALIGN=MIDDLE  ALT=\"PQ%5E2=%28-4%29%5E2%2B%28-6%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=PQ%5E2=16%2B36 ALIGN=MIDDLE  ALT=\"PQ%5E2=16%2B36\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=PQ%5E2=52 ALIGN=MIDDLE  ALT=\"PQ%5E2=52\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=QR%5E2=%282-8%29%5E2%2B%284-0%29%5E2 ALIGN=MIDDLE  ALT=\"QR%5E2=%282-8%29%5E2%2B%284-0%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=QR%5E2=36%2B16 ALIGN=MIDDLE  ALT=\"QR%5E2=36%2B16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=QR%5E2=52 ALIGN=MIDDLE  ALT=\"QR%5E2=52\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=PR%5E2=%28-2-8%29%5E2%2B%28-2-0%29%5E2 ALIGN=MIDDLE  ALT=\"PR%5E2=%28-2-8%29%5E2%2B%28-2-0%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=PR%5E2=%28-10%29%5E2%2B%28-2%29%5E2 ALIGN=MIDDLE  ALT=\"PR%5E2=%28-10%29%5E2%2B%28-2%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=PR%5E2=100%2B4 ALIGN=MIDDLE  ALT=\"PR%5E2=100%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=PR%5E2=104 ALIGN=MIDDLE  ALT=\"PR%5E2=104\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=PQ%5E2%2BQR%5E2=PR%5E2 ALIGN=MIDDLE  ALT=\"PQ%5E2%2BQR%5E2=PR%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=52%2B52=104 ALIGN=MIDDLE  ALT=\"52%2B52=104\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=104=104 ALIGN=MIDDLE  ALT=\"104=104\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Since the two sides are equal, the Pythagorean theorem holds and PQR is a right triangle.<BR>\n" );
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document.write( "c.) The legs of an isoceles triangle are congruent. <BR>\n" );
document.write( "Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=PQ%5E2=QR%5E2 ALIGN=MIDDLE  ALT=\"PQ%5E2=QR%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=PQ=QR ALIGN=MIDDLE  ALT=\"PQ=QR\"   DISABLED_style= \"max-width:90%; height:auto;\" > so this right triangle is also an isoceles triangle. <BR>\n" );
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