document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1178012>Question 1178012</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The coordinates of the point P,Q,R are (-1,11),(2,5) and (t,3) respectively. Given that ∠PQR = 90 °, calculate the value of t. The line PQ is produced to S so that QS = PQ. Calculate the coordinates of S. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #807205 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=807205\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "P,Q,R are (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1 ALIGN=MIDDLE  ALT=\"-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=11 ALIGN=MIDDLE  ALT=\"11\"   DISABLED_style= \"max-width:90%; height:auto;\" > ),(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5 ALIGN=MIDDLE  ALT=\"5\"   DISABLED_style= \"max-width:90%; height:auto;\" > ) and (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t ALIGN=MIDDLE  ALT=\"t\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" > ) respectively\r<BR>\n" );
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document.write( "first find the slope of the line passes through <BR>\n" );
document.write( "P(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1 ALIGN=MIDDLE  ALT=\"-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=11 ALIGN=MIDDLE  ALT=\"11\"   DISABLED_style= \"max-width:90%; height:auto;\" > ) and Q(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5 ALIGN=MIDDLE  ALT=\"5\"   DISABLED_style= \"max-width:90%; height:auto;\" > )\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=%285-11%29%2F%282-%28-1%29%29=-6%2F3=-2 ALIGN=MIDDLE  ALT=\"m=%285-11%29%2F%282-%28-1%29%29=-6%2F3=-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-2x%2Bb ALIGN=MIDDLE  ALT=\"y=-2x%2Bb\"   DISABLED_style= \"max-width:90%; height:auto;\" >....use one point to calculate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b ALIGN=MIDDLE  ALT=\"b\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5=-2%2A2%2Bb ALIGN=MIDDLE  ALT=\"5=-2%2A2%2Bb\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=5%2B4 ALIGN=MIDDLE  ALT=\"b=5%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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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;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-2x%2B9 ALIGN=MIDDLE  ALT=\"y=-2x%2B9\"   DISABLED_style= \"max-width:90%; height:auto;\" >.....eq.1\r<BR>\n" );
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document.write( "since given that ∠<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=PQR+=+90 ALIGN=MIDDLE  ALT=\"PQR+=+90\"   DISABLED_style= \"max-width:90%; height:auto;\" > °, find a line that is perpendicular  to line with a 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;\" > and passes through Q and R\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=mx%2Bb ALIGN=MIDDLE  ALT=\"y=mx%2Bb\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "the slope of the perpendicular line will be negative reciprocal of the 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;\" > and it is\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=-1%2F-2=1%2F2 ALIGN=MIDDLE  ALT=\"m=-1%2F-2=1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%281%2F2%29x%2Bb ALIGN=MIDDLE  ALT=\"y=%281%2F2%29x%2Bb\"   DISABLED_style= \"max-width:90%; height:auto;\" >...use one point to calculate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b ALIGN=MIDDLE  ALT=\"b\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5=%281%2F2%292%2Bb ALIGN=MIDDLE  ALT=\"5=%281%2F2%292%2Bb\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5=1%2Bb ALIGN=MIDDLE  ALT=\"5=1%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=4 ALIGN=MIDDLE  ALT=\"b=4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%281%2F2%29x%2B4 ALIGN=MIDDLE  ALT=\"y=%281%2F2%29x%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" >.....eq.2\r<BR>\n" );
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document.write( "since given (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t ALIGN=MIDDLE  ALT=\"t\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" > ), we use line<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y=3 ALIGN=MIDDLE  ALT=\"+y=3\"   DISABLED_style= \"max-width:90%; height:auto;\" > and the intersection point of the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%281%2F2%29x%2B4 ALIGN=MIDDLE  ALT=\"y=%281%2F2%29x%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y=3 ALIGN=MIDDLE  ALT=\"+y=3\"   DISABLED_style= \"max-width:90%; height:auto;\" > will have <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=t ALIGN=MIDDLE  ALT=\"x=t\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%281%2F2%29x%2B4 ALIGN=MIDDLE  ALT=\"y=%281%2F2%29x%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" >...substitute <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y ALIGN=MIDDLE  ALT=\"+y\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3=%281%2F2%29x%2B4 ALIGN=MIDDLE  ALT=\"3=%281%2F2%29x%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3-4=%281%2F2%29x ALIGN=MIDDLE  ALT=\"3-4=%281%2F2%29x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%2A2=x ALIGN=MIDDLE  ALT=\"-1%2A2=x\"   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;\" >=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=-2 ALIGN=MIDDLE  ALT=\"t=-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and the point <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R ALIGN=MIDDLE  ALT=\"R\"   DISABLED_style= \"max-width:90%; height:auto;\" >(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2 ALIGN=MIDDLE  ALT=\"-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" > ) \r<BR>\n" );
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document.write( "given also: the line<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+PQ ALIGN=MIDDLE  ALT=\"+PQ\"   DISABLED_style= \"max-width:90%; height:auto;\" > is produced to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S ALIGN=MIDDLE  ALT=\"S\"   DISABLED_style= \"max-width:90%; height:auto;\" > so that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=QS+=+PQ ALIGN=MIDDLE  ALT=\"QS+=+PQ\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Calculate the coordinates of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S ALIGN=MIDDLE  ALT=\"S\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S ALIGN=MIDDLE  ALT=\"S\"   DISABLED_style= \"max-width:90%; height:auto;\" > will be on a line <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%281%2F2%29x%2B4 ALIGN=MIDDLE  ALT=\"y=%281%2F2%29x%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" >, from  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Q ALIGN=MIDDLE  ALT=\"Q\"   DISABLED_style= \"max-width:90%; height:auto;\" > same distance as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+PQ ALIGN=MIDDLE  ALT=\"+PQ\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=sqrt%28%282-%28-1%29%29%5E2%2B%285-11%29%5E2%29 ALIGN=MIDDLE  ALT=\"d=sqrt%28%282-%28-1%29%29%5E2%2B%285-11%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=sqrt%283%5E2%2B%28-6%29%5E2%29 ALIGN=MIDDLE  ALT=\"d=sqrt%283%5E2%2B%28-6%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "distance is  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=sqrt%2845%29=6.7 ALIGN=MIDDLE  ALT=\"d=sqrt%2845%29=6.7\"   DISABLED_style= \"max-width:90%; height:auto;\" > which is radius <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r ALIGN=MIDDLE  ALT=\"r\"   DISABLED_style= \"max-width:90%; height:auto;\" > of the circle that passes through P, Q, and S\r<BR>\n" );
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document.write( "use the radius , draw a circle and read from the graph what are the  coordinates of the point S\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing+%28+600%2C+600%2C+-10%2C+15%2C+-10%2C+15%2C%0D%0Acircle%28-1%2C11%2C.12%29%2C+locate%28-1%2C11%2CP%28-1%2C11%29%29%2C%0D%0Acircle%282%2C5%2C.12%29%2C+locate%282%2C5%2CQ%282%2C5%29%29%2C%0D%0Acircle%28-2%2C3%2C.12%29%2C+locate%28-2%2C3%2CR%28-2%2C3%29%29%2C%0D%0Acircle%282%2C5%2Csqrt%2845%29%29%2Cblue%28line%282%2C5%2C-1%2C11%29%29%2C%0D%0Agreen%28line%28-2%2C3%2C-1%2C11%29%29%2Ccircle%28-4%2C2%2C.12%29%2Clocate%28-4.3%2C2%2CS%28-4%2C2%29%29%2C%0D%0Agraph%28+600%2C+600%2C+-10%2C+15%2C+-10%2C+15%2C3+%2C-2x%2B9%2C+x%2F2%2B4%29%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S ALIGN=MIDDLE  ALT=\"S\"   DISABLED_style= \"max-width:90%; height:auto;\" >(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4 ALIGN=MIDDLE  ALT=\"-4\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" > ) \r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );