document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1123420>Question 1123420</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Show that the points (12,9),(20,-6),(5,-14), and (-3,1) are the vertices of a square. What is the length of the diagonal?\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 #739765 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><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=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=739765\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Look at the distances of each of these from each other using the distance formula d=sqrt(chg x^2+chg y^2)<BR>\n" );
document.write( "sqrt (289) for the first pair and for the adjacent pairs so sides are equal.<BR>\n" );
document.write( "The pairs should have orthogonal or perpendicular slopes<BR>\n" );
document.write( "the first pair -15/8<BR>\n" );
document.write( "the second pair -8/-15 or 8/15, so they are perpendicular<BR>\n" );
document.write( "and the other pairs do likewise.<BR>\n" );
document.write( "Therefore, the diagonals are (12, 9) and (5, -14) and because it is a square, they should be sqrt(2)*s in length or sqrt(578)<BR>\n" );
document.write( "The distance between those two points is sqrt (49+23^2) or sqrt (578)<BR>\n" );
document.write( "Doing (20, -6) and (-3, 1) gives the same sqrt (578) distance.<BR>\n" );
document.write( "These points are the vertices of a square.<BR>\n" );
document.write( "The sides are equal<BR>\n" );
document.write( "The sides are perpendicular<BR>\n" );
document.write( "The diagonals are s*sqrt(2) more than the sides. </SPAN>\n" );
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