document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=983311>Question 983311</A>: <I><SPAN STYLE=\"word-break: break-all;\"> find the point(s)P on the xaxis in which the line through g(-4,-3) and P is perpendicular to the line through h(4,9) and P.   </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #604187 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39620)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=604187\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> (After drawing a graph on a chalkboard and thinking very carefully on this, a solution method began to come to me...)\r<BR>\n" );
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document.write( "Draw and label a graph of the situation as completely as you can do.<BR>\n" );
document.write( "Show your points G(-4,-3) and H(4,9); and judge what two points (x,y) on the x-axis would form two possible points P(x,y), so that you can draw lines.\r<BR>\n" );
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document.write( "The four points  (two different \"P\"), and G and H will form a trapezoidal figure.  Place your two \"P\" points so that PG and PH LOOK AS THOUGH they meet at right angle, or are perpendicular.\r<BR>\n" );
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document.write( "You will use the slopes of GP and PH.<BR>\n" );
document.write( "Perpendicular lines will have slopes which are negative reciprocals of each other.<BR>\n" );
document.write( "(You really need to know formula for slope of a line for this!)\r<BR>\n" );
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document.write( "Setup this table.\r<BR>\n" );
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document.write( "SLOPE________________EXPRESSION<BR>\n" );
document.write( "Line GP______________<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y%2B3%29%2F%28x%2B4%29 ALIGN=MIDDLE  ALT=\"%28y%2B3%29%2F%28x%2B4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Line PH______________<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y-9%29%2F%28x-4%29 ALIGN=MIDDLE  ALT=\"%28y-9%29%2F%28x-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Again, these slopes must form a product of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1 ALIGN=MIDDLE  ALT=\"-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "Next setup the equation for this:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%28%28%28y%2B3%29%2F%28x%2B4%29%29%28%28y-9%29%2F%28x-4%29%29=-1%29 ALIGN=MIDDLE  ALT=\"highlight_green%28%28%28y%2B3%29%2F%28x%2B4%29%29%28%28y-9%29%2F%28x-4%29%29=-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "I here omit a few steps...<BR>\n" );
document.write( "but you should get a step continuing with<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2-6y-27=-x%5E2%2B16 ALIGN=MIDDLE  ALT=\"y%5E2-6y-27=-x%5E2%2B16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and then continuing,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2-6y%2Bx%5E2=27%2B16 ALIGN=MIDDLE  ALT=\"y%5E2-6y%2Bx%5E2=27%2B16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2By%5E2-6y=43 ALIGN=MIDDLE  ALT=\"x%5E2%2By%5E2-6y=43\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "You also MUST know about Completing the Square  (maybe, maybe not...)<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%28x%5E2%2B%28y-3%29%5E2=52%29 ALIGN=MIDDLE  ALT=\"highlight_green%28x%5E2%2B%28y-3%29%5E2=52%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "That looks like it will be complicated to find your point P(x,y); but remember you are looking for possible points ON THE x-AXIS, and therefore <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28highlight%28y=0%29%29 ALIGN=MIDDLE  ALT=\"highlight%28highlight%28y=0%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "NOW, what is x?   </SPAN>\n" );
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