document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=943382>Question 943382</A>: <I><SPAN STYLE=\"word-break: break-all;\"> the coordinates of vertices X and Y of an equilateral XYZ are (-4,0) and (4,0), respectively. the coordinates of Z may be what?<BR>\n" );
document.write( " \r<BR>\n" );
document.write( "\n" );
document.write( "               I would like step-by-step process how you did this problem. thank you very much. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #575140 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=575140\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The coordinates of vertices X and Y of an equilateral XYZ are (-4,0) and (4,0), respectively. the coordinates of Z may be what?\r<BR>\n" );
document.write( "\n" );
document.write( "Solution:<BR>\n" );
document.write( "The slope of the line containing the segment XZ is equal to [tan (60 degrees)] = <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 x-intercept is -4, so the equation of the line XZ is <BR>\n" );
document.write( "y = <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;\" >x + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4sqrt%283%29 ALIGN=MIDDLE  ALT=\"4sqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
document.write( "\n" );
document.write( "The slope of the line containing YZ is numerically equal to the slope of XZ but opposite in sign. The x-intercept is 4, so the equation of the line YZ is <BR>\n" );
document.write( "y = <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;\" >x + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4sqrt%283%29 ALIGN=MIDDLE  ALT=\"4sqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
document.write( "\n" );
document.write( "To get the coordinates of Z, we solve for the intersection of the lines XZ and YZ.<BR>\n" );
document.write( "<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;\" >x + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4sqrt%283%29 ALIGN=MIDDLE  ALT=\"4sqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <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;\" >x + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4sqrt%283%29 ALIGN=MIDDLE  ALT=\"4sqrt%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%29 ALIGN=MIDDLE  ALT=\"2sqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >x = 0<BR>\n" );
document.write( "x = 0<BR>\n" );
document.write( "Therefore, y = <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;\" >(0) + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4sqrt%283%29 ALIGN=MIDDLE  ALT=\"4sqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4sqrt%283%29 ALIGN=MIDDLE  ALT=\"4sqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The coordinates of Z are (0, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4sqrt%283%29 ALIGN=MIDDLE  ALT=\"4sqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >) [Answer]<BR>\n" );
document.write( "By symmetry, the other possible answer is (0, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4sqrt%283%29 ALIGN=MIDDLE  ALT=\"-4sqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );