document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1055984>Question 1055984</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Can you help me in solving this problem:<BR>\n" );
document.write( "Starting with the graph of y=2x,  write the equation of the graph that results from \r<BR>\n" );
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document.write( "(a) reflecting about the line y=4<BR>\n" );
document.write( "(b) reflecting about the line x=2<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #671169 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><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=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=671169\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> (a)<BR>\n" );
document.write( "The reflection about <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;\" > ( a horizontal line )<BR>\n" );
document.write( "Must be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+4+%2B+4+=+8+ ALIGN=MIDDLE  ALT=\"+4+%2B+4+=+8+\"   DISABLED_style= \"max-width:90%; height:auto;\" > units along y-axis from ( 0,0 )<BR>\n" );
document.write( "which <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+2x+ ALIGN=MIDDLE  ALT=\"+y+=+2x+\"   DISABLED_style= \"max-width:90%; height:auto;\" > goes through<BR>\n" );
document.write( "This point is ( 0, 8 )<BR>\n" );
document.write( "----------------------------<BR>\n" );
document.write( "The intercept at <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;\" > is <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+2x+ ALIGN=MIDDLE  ALT=\"+y+=+2x+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+4+=+2x+ ALIGN=MIDDLE  ALT=\"+4+=+2x+\"   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( "( 2,4 ) , which stays the same for reflected line<BR>\n" );
document.write( "------------------------------------------<BR>\n" );
document.write( "The slope goes through these 2 points and must have<BR>\n" );
document.write( "the negative of the slope of the given line.<BR>\n" );
document.write( "Now use the general point-slope formula<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28+y+-+4+%29+%2F+%28+x+-+2+%29+=+%28+8+-+4+%29+%2F+%28+0+-+2+%29+ ALIGN=MIDDLE  ALT=\"+%28+y+-+4+%29+%2F+%28+x+-+2+%29+=+%28+8+-+4+%29+%2F+%28+0+-+2+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28+y+-+4+%29+%2F+%28+x+-+2+%29+=+4+%2F+%28-2%29+ ALIGN=MIDDLE  ALT=\"+%28+y+-+4+%29+%2F+%28+x+-+2+%29+=+4+%2F+%28-2%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28+y+-+4+%29+%2F+%28+x+-+2+%29+=+-2+ ALIGN=MIDDLE  ALT=\"+%28+y+-+4+%29+%2F+%28+x+-+2+%29+=+-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+-+4+=+-2%2A%28+x+-+2+%29+ ALIGN=MIDDLE  ALT=\"+y+-+4+=+-2%2A%28+x+-+2+%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+-+4+=+-2x+%2B+4+ ALIGN=MIDDLE  ALT=\"+y+-+4+=+-2x+%2B+4+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+-2x+%2B+8+ ALIGN=MIDDLE  ALT=\"+y+=+-2x+%2B+8+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "( note that I get the correct slope, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-2+ ALIGN=MIDDLE  ALT=\"+-2+\"   DISABLED_style= \"max-width:90%; height:auto;\" > )<BR>\n" );
document.write( "----------------------<BR>\n" );
document.write( "Here's the plot of the 2 lines:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+400%2C+400%2C+-10%2C+10%2C+-10%2C+10%2C+2x%2C+4%2C+-2x+%2B+8+%29+ ALIGN=MIDDLE  ALT=\"+graph%28+400%2C+400%2C+-10%2C+10%2C+-10%2C+10%2C+2x%2C+4%2C+-2x+%2B+8+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-------------------------------------------------------<BR>\n" );
document.write( "(b)<BR>\n" );
document.write( "Reflected about <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( "This is a vertical line through ( 2, 0 )<BR>\n" );
document.write( "The reflection of ( 0,0 ) would be ( 4,0 )<BR>\n" );
document.write( "-------------------------------------<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+2x+ ALIGN=MIDDLE  ALT=\"+y+=+2x+\"   DISABLED_style= \"max-width:90%; height:auto;\" > intercepts <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;\" > at ( 2,4 )<BR>\n" );
document.write( "The reflection is at the same point ( 2,4 )<BR>\n" );
document.write( "-----------------------------------------------<BR>\n" );
document.write( "Again, I should end up with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-2+ ALIGN=MIDDLE  ALT=\"+-2+\"   DISABLED_style= \"max-width:90%; height:auto;\" > for a slope<BR>\n" );
document.write( "Use general point-slope formula<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28+y+-+0+%29+%2F+%28+x+-+4+%29+=+%28+4+-+0+%29+%2F+%28+2+-+4+%29+ ALIGN=MIDDLE  ALT=\"+%28+y+-+0+%29+%2F+%28+x+-+4+%29+=+%28+4+-+0+%29+%2F+%28+2+-+4+%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+%2F+%28+x+-+4+%29+=+4%2F%28-2%29+ ALIGN=MIDDLE  ALT=\"+y+%2F+%28+x+-+4+%29+=+4%2F%28-2%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+%2F+%28+x+-+4+%29+=+-2+ ALIGN=MIDDLE  ALT=\"+y+%2F+%28+x+-+4+%29+=+-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+=+-2%2A%28+x+-+4+%29+ ALIGN=MIDDLE  ALT=\"+y+=+-2%2A%28+x+-+4+%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+=+-2x+%2B+8+ ALIGN=MIDDLE  ALT=\"+y+=+-2x+%2B+8+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "This is the same line as in previous problem.<BR>\n" );
document.write( "so, it doesn't matter whether you use <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( "of <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;\" > for a reflection.<BR>\n" );
document.write( "--------------<BR>\n" );
document.write( "Definitely get a 2nd opinion on this, it looks right<BR>\n" );
document.write( "to me, but it's a little tricky\r<BR>\n" );
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document.write( "  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );