document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=228481>Question 228481</A>: <I><SPAN STYLE=\"word-break: break-all;\"> An equilateral triangle has 2 verticles at (0,-1) and (0,5) Find all possibilities for the third vertex.\r<BR>\n" );
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document.write( "I figured out the distance between the two points is 6 and I know that the thrid vertex can be in quadrant I and II, but I'm having trouble trying to use the distance formula figure out the coordinates of the 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 #169590 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=169590\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> An equilateral triangle has 2 verticles at (0,-1) and (0,5) Find all possibilities for the third vertex. <BR>\n" );
document.write( "I figured out the distance between the two points is 6 and I know that the thrid vertex can be in quadrant I and II, but I'm having trouble trying to use the distance formula figure out the coordinates of the vertex. <BR>\n" );
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document.write( "Let (x,y) be 6 from (0,-1)<BR>\n" );
document.write( "6^2 = (x-0)^2 + (y+1)^2<BR>\n" );
document.write( "36 = x^2 + y^2+2y+1<BR>\n" );
document.write( "A) 35 = x^2+y^2+2y<BR>\n" );
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document.write( "Let (x,y) be 6 from (0,5)<BR>\n" );
document.write( "6^2 = (x-0)^2 + (y-5)^2<BR>\n" );
document.write( "36 = x^2 + y^2-10y+25<BR>\n" );
document.write( "B) 9 = x^2 + y^2-10y<BR>\n" );
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document.write( "Subtract Equation B from Equation A and solve for \"y\":<BR>\n" );
document.write( "16 = 12y<BR>\n" );
document.write( "y = 4/3<BR>\n" );
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document.write( "Sustitute into \"A\" to solve for \"x\":<BR>\n" );
document.write( "35 = x^2 + (16/9)+2(4/3)<BR>\n" );
document.write( "35 = x^2 + 16/9 + 24/9<BR>\n" );
document.write( "x^2 = 35 - (40/9)<BR>\n" );
document.write( "x^2 = 275/9<BR>\n" );
document.write( "x = (5/3)sqrt(11) or x = (-5/3)sqrt(11)\r<BR>\n" );
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document.write( "Vertices are ((5/3)sqrt(11),4/3) or ((-5/3)sqrt(11),4/3)<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
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