document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1139696>Question 1139696</A>: <I><SPAN STYLE=\"word-break: break-all;\"> triangle ABC is a right triangle. Sides AB and BC form the fight angle. The equation of the line is representing side AB is 4x+8y=16. If C is located at point (1,-3) What is the equation of the line representing side BC? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #760212 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=760212\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "A simplified form of the equation of the line containing AB is x+2y = 4.<br><BR>\n" );
document.write( "Since there is a right angle at B, CB will be a line perpendicular to AB and containing point (1,-3).<br><BR>\n" );
document.write( "One elementary way of solving the problem is to find the slope of AB, then find the slope of a line perpendicular to AB, then find the equation of the line with that slope containing (1,-3).<br><BR>\n" );
document.write( "I leave it to you to solve the problem that way if you choose.<br><BR>\n" );
document.write( "Here is a more advanced method for solving the problem.<br><BR>\n" );
document.write( "Every line parallel to the line x+2y=4 has an equation of the form x+2y=c for some constant c (the coefficients of x and y remain the same);<br><BR>\n" );
document.write( "Every line perpendicular to the line x+2y=4 has an equation of the form 2x-y=c for some constant c (the coefficients of x and y switch, and one of them changes sign).<br><BR>\n" );
document.write( "So the line containing BC has an equation of the form 2x-y=c.  Then, since that line contains the point (1,-3), we can easily determine the value of c:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x-y+=+2%281%29-%28-3%29+=+2%2B3+=+5+=+c ALIGN=MIDDLE  ALT=\"2x-y+=+2%281%29-%28-3%29+=+2%2B3+=+5+=+c\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "So an equation of the line containing side BC is<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x-y+=+5 ALIGN=MIDDLE  ALT=\"2x-y+=+5\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );