document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=870669>Question 870669</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Dear math tutor,\r<BR>\n" );
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document.write( "A(7,2) and C(1,4) are two vertices of a square ABCD. Find the equation of the diagonal BD. Find the coordinates of B and D.\r<BR>\n" );
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document.write( "with gratitude,<BR>\n" );
document.write( "nats </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #525105 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=525105\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C300%2C-2%2C10%2C-2%2C10%2Ccircle%287%2C2%2C0.2%29%2Ccircle%281%2C4%2C0.2%29%2Cline%287%2C2%2C1%2C4%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Find the slope of the line connecting A and C.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=%284-2%29%2F%281-7%29=2%2F-6=-1%2F3 ALIGN=MIDDLE  ALT=\"m=%284-2%29%2F%281-7%29=2%2F-6=-1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Diagonal BD is perpendicular to diagonal AC so their slopes are negative reciprocals of each other.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m%5Bperp%5D%2A%28-1%2F3%29=-1 ALIGN=MIDDLE  ALT=\"m%5Bperp%5D%2A%28-1%2F3%29=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m%7Bperp%5D=3 ALIGN=MIDDLE  ALT=\"m%7Bperp%5D=3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Diagonal BD also goes through the midpoint of AC. <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5Bm%5D=%287%2B1%29%2F2=8%2F2=4 ALIGN=MIDDLE  ALT=\"x%5Bm%5D=%287%2B1%29%2F2=8%2F2=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%5Bm%5D=%282%2B4%29%2F2=6%2F2=3 ALIGN=MIDDLE  ALT=\"y%5Bm%5D=%282%2B4%29%2F2=6%2F2=3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Use this point to find the line, BC, <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( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3=3%284%29%2Bb ALIGN=MIDDLE  ALT=\"3=3%284%29%2Bb\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=-9 ALIGN=MIDDLE  ALT=\"b=-9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=3x-9 ALIGN=MIDDLE  ALT=\"y=3x-9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C300%2C-2%2C10%2C-2%2C10%2Ccircle%287%2C2%2C0.2%29%2Ccircle%281%2C4%2C0.2%29%2Cline%287%2C2%2C1%2C4%29%2Cgraph%28300%2C300%2C-2%2C10%2C-2%2C10%2C3x-9%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( "The distance from the midpoint to points B and D is the same as the distance from the midpoint to A and C.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D%5E2=%287-4%29%5E2%2B%282-3%29%5E2 ALIGN=MIDDLE  ALT=\"D%5E2=%287-4%29%5E2%2B%282-3%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D%5E2=9%2B1 ALIGN=MIDDLE  ALT=\"D%5E2=9%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D%5E2=10 ALIGN=MIDDLE  ALT=\"D%5E2=10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The distance from the midpoint to B and D is,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10=%28x-4%29%5E2%2B%28y-3%29%5E2 ALIGN=MIDDLE  ALT=\"10=%28x-4%29%5E2%2B%28y-3%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "But you also know that B and D lie on the line <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=3x-9 ALIGN=MIDDLE  ALT=\"y=3x-9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So substituting.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10=%28x-4%29%5E2%2B%283x-9-3%29%5E2 ALIGN=MIDDLE  ALT=\"10=%28x-4%29%5E2%2B%283x-9-3%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10=x%5E2-8x%2B16%2B9x%5E2-72x%2B144 ALIGN=MIDDLE  ALT=\"10=x%5E2-8x%2B16%2B9x%5E2-72x%2B144\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10=10x%5E2-80x%2B160 ALIGN=MIDDLE  ALT=\"10=10x%5E2-80x%2B160\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10x%5E2-80x%2B150=0 ALIGN=MIDDLE  ALT=\"10x%5E2-80x%2B150=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-8x%2B15=0 ALIGN=MIDDLE  ALT=\"x%5E2-8x%2B15=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-3%29%28x-5%29=0 ALIGN=MIDDLE  ALT=\"%28x-3%29%28x-5%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Two solutions:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-3=0 ALIGN=MIDDLE  ALT=\"x-3=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=3 ALIGN=MIDDLE  ALT=\"x=3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Then<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=3%283%29-9 ALIGN=MIDDLE  ALT=\"y=3%283%29-9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=0 ALIGN=MIDDLE  ALT=\"y=0\"   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=x-5=0 ALIGN=MIDDLE  ALT=\"x-5=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=5 ALIGN=MIDDLE  ALT=\"x=5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Then,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=3%285%29-9 ALIGN=MIDDLE  ALT=\"y=3%285%29-9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=6 ALIGN=MIDDLE  ALT=\"y=6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "B and D are (3,0) and (5,6)<BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C300%2C-2%2C10%2C-2%2C10%2Ccircle%287%2C2%2C0.2%29%2Ccircle%281%2C4%2C0.2%29%2Ccircle%283%2C0%2C0.2%29%2Ccircle%285%2C6%2C0.2%29%2Cline%281%2C4%2C3%2C0%29%2Cline%283%2C0%2C7%2C2%29%2Cline%287%2C2%2C5%2C6%29%2Cline%285%2C6%2C1%2C4%29%2Cgraph%28300%2C300%2C-2%2C10%2C-2%2C10%2C3x-9%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " </SPAN>\n" );
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