document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1062846>Question 1062846</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Obtain the equation of a straight line that is symmetric to line l: y=x-3 with respect to line m: (-1/3)x-(1/3). </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #677942 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><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=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=677942\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> First find the point of intersection,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-3=-x%2F3-1%2F3 ALIGN=MIDDLE  ALT=\"x-3=-x%2F3-1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2Bx%2F3=3-1%2F3 ALIGN=MIDDLE  ALT=\"x%2Bx%2F3=3-1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284%2F3%29x=8%2F3 ALIGN=MIDDLE  ALT=\"%284%2F3%29x=8%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=2 ALIGN=MIDDLE  ALT=\"x=2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So then,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=2-3 ALIGN=MIDDLE  ALT=\"y=2-3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-1 ALIGN=MIDDLE  ALT=\"y=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now find the perpendicular bisector of the line, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-x%2F3-1%2F3 ALIGN=MIDDLE  ALT=\"y=-x%2F3-1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >}, <BR>\n" );
document.write( "you know that the slope of the bisector is equal to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=3 ALIGN=MIDDLE  ALT=\"m=3\"   DISABLED_style= \"max-width:90%; height:auto;\" > since perpendicular lines have slopes that are negative reciprocals.<BR>\n" );
document.write( "So the line has the form <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=3x%2Bb ALIGN=MIDDLE  ALT=\"y=3x%2Bb\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Choose a point on the line.<BR>\n" );
document.write( "I'll choose (5,-2). <BR>\n" );
document.write( "So the equation of the perpendicular bisector using point slope form would be,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%2B2=3%28x-5%29 ALIGN=MIDDLE  ALT=\"y%2B2=3%28x-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=3x-15-2 ALIGN=MIDDLE  ALT=\"y=3x-15-2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=3x-17 ALIGN=MIDDLE  ALT=\"y=3x-17\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The intersection point of the perpendicular bisector with the original line can be found,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-3=3x-17 ALIGN=MIDDLE  ALT=\"x-3=3x-17\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2x=-14 ALIGN=MIDDLE  ALT=\"-2x=-14\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=7 ALIGN=MIDDLE  ALT=\"x=7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=7-3 ALIGN=MIDDLE  ALT=\"y=7-3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=4 ALIGN=MIDDLE  ALT=\"y=4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(7,4)<BR>\n" );
document.write( "So then using (5,-2) as the center point and (7,4) as the intersection point, find the corresponding intersection point with the symmetric line. <BR>\n" );
document.write( "To go from the center point to the intersection point, you move 2 units in x and 6 units in y. The intersection point of the symmetric line will have the same value but just different sign. <BR>\n" );
document.write( "So starting at (5,-2) you would move -2 in the x and -6 in the y. <BR>\n" );
document.write( "(5,-2)+(-2,-6)=((3,-8)<BR>\n" );
document.write( "So now you know the symmetric line goes through (3,-8) and (2,-1). <BR>\n" );
document.write( "Find the slope,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=%28-8-%28-1%29%29%2F%283-2%29=-7 ALIGN=MIDDLE  ALT=\"m=%28-8-%28-1%29%29%2F%283-2%29=-7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Then use the point slope form,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-%28-8%29=-7%28x-3%29 ALIGN=MIDDLE  ALT=\"y-%28-8%29=-7%28x-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%2B8=7x%2B21 ALIGN=MIDDLE  ALT=\"y%2B8=7x%2B21\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28y=13-7x%29 ALIGN=MIDDLE  ALT=\"highlight%28y=13-7x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/display-illustration.mpl?tutor=Fombitz&illustration_name=AD1.jpg\"> </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );