document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1091561>Question 1091561</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Prove that the midpoint of a kite form a rectangle<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 #705976 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=705976\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br>This can be proved rather easily using coordinate geometry.  Suppose we situate the kite on the coordinate plane so that the intersection of the two diagonals is the origin.  According to the definition of a kite, we can call two of the vertices (-2a,0) and (2a,0), and the other two vertices (0,2b) and (0,2c) (where in my diagram b is positive and c is negative).<br><BR>\n" );
document.write( "Then the midpoints of the four sides are (-a,b), (a,b), (-a,d), and (a,d).<br><BR>\n" );
document.write( "The quadrilateral determined by those four points has two sides that are horizontal line segments and two sides that are vertical line segments; that makes the quadrilateral a rectangle. </SPAN>\n" );
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