document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=752201>Question 752201</A>: <I><SPAN STYLE=\"word-break: break-all;\"> if an equilateraltriangle has 2 coordinates (-2,0),(2,0) find the third vertex?\r<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 #457625 by </B><A HREF=/tutors/aboutme.mpl?userid=reviewermath><B>reviewermath(1029)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=reviewermath><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=reviewermath><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=457625\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Q: if an equilateral triangle has 2 coordinates (-2,0),(2,0) find the third vertex?<BR>\n" );
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document.write( "A: The slope of the line segment joining (-2,0) and the third vertex is tan 60° = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%283%29 ALIGN=MIDDLE  ALT=\"sqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. The equation of the line segment is <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+-+0+=+sqrt%283%29%28x+-+%28-2%29%29 ALIGN=MIDDLE  ALT=\"y+-+0+=+sqrt%283%29%28x+-+%28-2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+sqrt%283%29x+%2B+2sqrt%283%29 ALIGN=MIDDLE  ALT=\"y+=+sqrt%283%29x+%2B+2sqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "The slope of the line segment joining (2,0) and the third vertex is tan -60° = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-sqrt%283%29 ALIGN=MIDDLE  ALT=\"-sqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. The equation of the 2nd line segment is <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+-+0+=+-sqrt%283%29%28x+-+2%29 ALIGN=MIDDLE  ALT=\"y+-+0+=+-sqrt%283%29%28x+-+2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+-sqrt%283%29x+%2B+2sqrt%283%29 ALIGN=MIDDLE  ALT=\"y+=+-sqrt%283%29x+%2B+2sqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "To find the third vertex, we get the point of intersection of the two line segments. By using substitution method:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%283%29x+%2B+2sqrt%283%29 ALIGN=MIDDLE  ALT=\"sqrt%283%29x+%2B+2sqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-sqrt%283%29x+%2B+2sqrt%283%29 ALIGN=MIDDLE  ALT=\"+-sqrt%283%29x+%2B+2sqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2sqrt%283%29x+ ALIGN=MIDDLE  ALT=\"2sqrt%283%29x+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 0<BR>\n" );
document.write( "x = 0, substitute in the first equation<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+sqrt%283%29%280%29+%2B+2sqrt%283%29 ALIGN=MIDDLE  ALT=\"y+=+sqrt%283%29%280%29+%2B+2sqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2sqrt%283%29 ALIGN=MIDDLE  ALT=\"2sqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Third Vertex: (0, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2sqrt%283%29 ALIGN=MIDDLE  ALT=\"2sqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
document.write( "There are two possible answers, by symmetry, the other possible answer is (0, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2sqrt%283%29 ALIGN=MIDDLE  ALT=\"-2sqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
document.write( "ANSWERS: (0, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2sqrt%283%29 ALIGN=MIDDLE  ALT=\"2sqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >) OR (0, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2sqrt%283%29 ALIGN=MIDDLE  ALT=\"-2sqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >) </SPAN>\n" );
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