document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1015593>Question 1015593</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Complex numbers/trig:<BR>\n" );
document.write( "Two isosceles right triangles (BAC and B'AC'; A is the right angle) share vertex A. Show that that the line bisecting line BB', passing through A is perpendicular to line CC'.<BR>\n" );
document.write( "(B and B' and (C and C') are on the same side, to be clearer) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #632128 by </B><A HREF=/tutors/aboutme.mpl?userid=richard1234><B>richard1234(7193)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=richard1234><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=richard1234><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=632128\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let A = 0, B = i, C = 1, B' = a+bi for real a,b, and C' = i(a+bi) = -b + ai. Here i(a+bi) represents a 45 degree rotation about point A.\r<BR>\n" );
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document.write( "The midpoint of BB' is (a+(b+1)i)/2, and the slope of the line bisecting BB' through A is (b+1)/a.\r<BR>\n" );
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document.write( "Line CC' has slope (0-a)/(1+b) = -a/(b+1).\r<BR>\n" );
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document.write( "Since the product of the two slopes is -1, the two lines are perpendicular. </SPAN>\n" );
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