document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=550586>Question 550586</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1.(a)If (p+1)x+y=3 and 3y-(p-1)x=4 are perpendicular to each other,find the value of p.<BR>\n" );
document.write( "(b)If y+(2p+1)x+3=0 and 8y-(2p-1)x=5 are mutually perpendicular,find the value of p.<BR>\n" );
document.write( "2.The co-ordinates of the vertex A of a square ABCD are (1,2) and the equation of the diagonal BD is x+2y=10.Find the equation of the other diagonal and the co-ordinates of the centre of the square.<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #359069 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=359069\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1.(a)If (p+1)x+y=3 and 3y-(p-1)x=4 are perpendicular to each other, the product of their slopes is -1. I can use that fact to find the value of p.<BR>\n" );
document.write( "The slope of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28p%2B1%29x%2By=3 ALIGN=MIDDLE  ALT=\"%28p%2B1%29x%2By=3\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-%28p%2B1%29x%2B3 ALIGN=MIDDLE  ALT=\"y=-%28p%2B1%29x%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-%28p%2B1%29 ALIGN=MIDDLE  ALT=\"-%28p%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The slope of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3y-%28p-1%29x=4 ALIGN=MIDDLE  ALT=\"3y-%28p-1%29x=4\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3y=%28p-1%29x%2B4 ALIGN=MIDDLE  ALT=\"3y=%28p-1%29x%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28p-1%29x%2F3%2B4%2F3 ALIGN=MIDDLE  ALT=\"y=%28p-1%29x%2F3%2B4%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28p-1%29%2F3 ALIGN=MIDDLE  ALT=\"%28p-1%29%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The product of the slopes is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-%28p%2B1%29%28p-1%29%2F3=-1 ALIGN=MIDDLE  ALT=\"-%28p%2B1%29%28p-1%29%2F3=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28p%2B1%29%28p-1%29=3 ALIGN=MIDDLE  ALT=\"%28p%2B1%29%28p-1%29=3\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%5E2-1=3 ALIGN=MIDDLE  ALT=\"p%5E2-1=3\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%5E2=4 ALIGN=MIDDLE  ALT=\"p%5E2=4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "There are two solutions <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p=2 ALIGN=MIDDLE  ALT=\"p=2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p=-2 ALIGN=MIDDLE  ALT=\"p=-2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(b)If y+(2p+1)x+3=0 and 8y-(2p-1)x=5 are mutually perpendicular, the product of their slopes is -1. I can use that fact to find the value of p.<BR>\n" );
document.write( "The slope of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%2B%282p%2B1%29x%2B3=0 ALIGN=MIDDLE  ALT=\"y%2B%282p%2B1%29x%2B3=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-%282p%2B1%29x-3 ALIGN=MIDDLE  ALT=\"y=-%282p%2B1%29x-3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-%282p%2B1%29 ALIGN=MIDDLE  ALT=\"-%282p%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The slope of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8y-%282p-1%29x=5 ALIGN=MIDDLE  ALT=\"8y-%282p-1%29x=5\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8y=%282p-1%29x%2B5 ALIGN=MIDDLE  ALT=\"8y=%282p-1%29x%2B5\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%282p-1%29x%2F8%2B5%2F8 ALIGN=MIDDLE  ALT=\"y=%282p-1%29x%2F8%2B5%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282p-1%29%2F8 ALIGN=MIDDLE  ALT=\"%282p-1%29%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The product of the slopes is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-%282p%2B1%29%282p-1%29%2F8=-1 ALIGN=MIDDLE  ALT=\"-%282p%2B1%29%282p-1%29%2F8=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282p%2B1%29%282p-1%29=8 ALIGN=MIDDLE  ALT=\"%282p%2B1%29%282p-1%29=8\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4p%5E2-1=8 ALIGN=MIDDLE  ALT=\"4p%5E2-1=8\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4p%5E2=9 ALIGN=MIDDLE  ALT=\"4p%5E2=9\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%5E2=9%2F4 ALIGN=MIDDLE  ALT=\"p%5E2=9%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "There are two solutions <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p=3%2F2 ALIGN=MIDDLE  ALT=\"p=3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p=-3%2F2 ALIGN=MIDDLE  ALT=\"p=-3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "2.The co-ordinates of the vertex A of a square ABCD are (1,2) and the equation of the diagonal BD is x+2y=10.Find the equation of the other diagonal and the co-ordinates of the centre of the square.<BR>\n" );
document.write( "I solved this problem recently. It was submitted as question # 550393. </SPAN>\n" );
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