document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=848023>Question 848023</A>: <I><SPAN STYLE=\"word-break: break-all;\"> P(-3,1), Q(2,5) and R(7,a) are three points in the cartesian plane. Find the values of ''a'' in each case if<BR>\n" );
document.write( "P,Q and R are collinear<BR>\n" );
document.write( "PQR=90 degrees<BR>\n" );
document.write( "PR=QR </SPAN>\n" );
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document.write( "First find equation of line PQ.<BR>\n" );
document.write( "Slope <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=%285-1%29%2F%282-%28-3%29%29=4%2F5 ALIGN=MIDDLE  ALT=\"m=%285-1%29%2F%282-%28-3%29%29=4%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >;<BR>\n" );
document.write( "y=mx+b<BR>\n" );
document.write( "b=y-mx<BR>\n" );
document.write( "Use the point P or Q, find b value.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=5-%284%2F5%292=5-8%2F5=25%2F5-8%2F5=17%2F5 ALIGN=MIDDLE  ALT=\"b=5-%284%2F5%292=5-8%2F5=25%2F5-8%2F5=17%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >;<BR>\n" );
document.write( "Equation for PQ is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28y=%284%2F5%29x%2B17%2F5%29 ALIGN=MIDDLE  ALT=\"highlight%28y=%284%2F5%29x%2B17%2F5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
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document.write( "R is collinear:  Use x=7 to find \"a\".--------<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%284%2F5%29%2A7%2B17%2F5 ALIGN=MIDDLE  ALT=\"y=%284%2F5%29%2A7%2B17%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=28%2F5%2B17%2F5=highlight%2842%2F5%29 ALIGN=MIDDLE  ALT=\"y=28%2F5%2B17%2F5=highlight%2842%2F5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "Point R(7, 42/5) Collinear with P and Q.\r<BR>\n" );
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document.write( "PQR to be 90 degree---<BR>\n" );
document.write( "That is perpendicular to eachother, PQ and QR.<BR>\n" );
document.write( "The line QR would have slope <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=-5%2F4 ALIGN=MIDDLE  ALT=\"m=-5%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "The line for QR in this way, which will contain Q, will be y=-(5/4)x+b; here, this b is going to be different from the one for PQ.<BR>\n" );
document.write( "b=y+(5/4)x<BR>\n" );
document.write( "and using point Q(2, 5),<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=5%2B%285%2F4%292=5%2B10%2F4=20%2F4%2B10%2F4=30%2F4=15%2F2 ALIGN=MIDDLE  ALT=\"b=5%2B%285%2F4%292=5%2B10%2F4=20%2F4%2B10%2F4=30%2F4=15%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "Line QR is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28y=-%285%2F4%29x%2B15%2F2%29 ALIGN=MIDDLE  ALT=\"highlight%28y=-%285%2F4%29x%2B15%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
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document.write( "What then is R?  What is y when x=7?<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-%285%2F4%29%2A7%2B15%2F2 ALIGN=MIDDLE  ALT=\"y=-%285%2F4%29%2A7%2B15%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-35%2F4%2B15%2F2=-35%2F4%2B30%2F4=-5%2F4 ALIGN=MIDDLE  ALT=\"y=-35%2F4%2B15%2F2=-35%2F4%2B30%2F4=-5%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Point R is (7, -5/4).\r<BR>\n" );
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document.write( "PR=QR-------<BR>\n" );
document.write( "Use the distance formula for PR and QR.  The variable will be a.<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=PR=sqrt%28%287-%28-3%29%29%5E2%2B%28a-1%29%5E2%29 ALIGN=MIDDLE  ALT=\"PR=sqrt%28%287-%28-3%29%29%5E2%2B%28a-1%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=sqrt%28100%2Ba%5E2-2a%2B1%29 ALIGN=MIDDLE  ALT=\"sqrt%28100%2Ba%5E2-2a%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28a%5E2-2a%2B101%29 ALIGN=MIDDLE  ALT=\"sqrt%28a%5E2-2a%2B101%29\"   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=QR=sqrt%28%287-2%29%5E2%2B%28a-5%29%5E2%29 ALIGN=MIDDLE  ALT=\"QR=sqrt%28%287-2%29%5E2%2B%28a-5%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=sqrt%2825%2Ba%5E2-10a%2B25%29 ALIGN=MIDDLE  ALT=\"sqrt%2825%2Ba%5E2-10a%2B25%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28a%5E2-10a%2B50%29 ALIGN=MIDDLE  ALT=\"sqrt%28a%5E2-10a%2B50%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Equating PR=QR and squaring both sides gives<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%28a%5E2-2a%2B101=a%5E2-10a%2B50%29 ALIGN=MIDDLE  ALT=\"highlight_green%28a%5E2-2a%2B101=a%5E2-10a%2B50%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "-...<BR>\n" );
document.write( "You continue this to find a? </SPAN>\n" );
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