document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=650919>Question 650919</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Determine whether the three points are collinear.<BR>\n" );
document.write( "(5,-1), (-3,6), (4,-2) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #407481 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=407481\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "Three or more points <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P1 ALIGN=MIDDLE  ALT=\"P1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P2 ALIGN=MIDDLE  ALT=\"P2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P3 ALIGN=MIDDLE  ALT=\"P3\"   DISABLED_style= \"max-width:90%; height:auto;\" > are said to be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=collinear ALIGN=MIDDLE  ALT=\"collinear\"   DISABLED_style= \"max-width:90%; height:auto;\" > <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=if ALIGN=MIDDLE  ALT=\"if\"   DISABLED_style= \"max-width:90%; height:auto;\" > they <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=lie ALIGN=MIDDLE  ALT=\"lie\"   DISABLED_style= \"max-width:90%; height:auto;\" > on a <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=single ALIGN=MIDDLE  ALT=\"single\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+straight ALIGN=MIDDLE  ALT=\"+straight\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+line ALIGN=MIDDLE  ALT=\"+line\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+L ALIGN=MIDDLE  ALT=\"+L\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "let's check it:\r<BR>\n" );
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document.write( " <TR><TD  ALIGN=MIDDLE>Solved by <A  rel=nofollow HREF=http://wiki.algebra.com/index.php/Tutoring_-_pluggable_solvers>pluggable</A> solver: <A  rel=nofollow HREF=To_determine_if_3_points_lie_in_a_line.solver>To determine if 3 points lie in a line</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT> The 3 points lie on a same plane. For all points to lie on a line they should satisfy the <A  rel=nofollow HREF=http://www.algebra.com/algebra/homework/Linear-equations/Polynomial-Expressions-and-Equations-in-Color.lesson>equation of a line</A>. Hence any two points taken on a line should calculate to the same slope of a line.<BR>\n" );
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document.write( "  In order to prove the 3 points to lie on a line, as there exists a unique line containing three points and every line has a unique <A  rel=nofollow HREF=http://www.algebra.com/algebra/homework/Graphs/slope.wikipedia>slope</A>. <BR>\n" );
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document.write( "  Hence it will be sufficient to prove that the slope calculated taking 2 points at a time should be equal.<BR>\n" );
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document.write( "  Slope of line taking points (X1,Y1) and (X2,Y2) is<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=slope+=+%28Y2-Y1%29%2F%28X2-X1%29 ALIGN=MIDDLE  ALT=\"slope+=+%28Y2-Y1%29%2F%28X2-X1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=slope+=+%28%286--1%29%2F%28-3-5%29%29+=+-0.875 ALIGN=MIDDLE  ALT=\"slope+=+%28%286--1%29%2F%28-3-5%29%29+=+-0.875\"   DISABLED_style= \"max-width:90%; height:auto;\" >     ........................(1)<BR>\n" );
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document.write( "  Slope of line taking points (X3,Y3) and (X1,Y1) is<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=slope+=+%28Y3-Y1%29%2F%28X3-X1%29 ALIGN=MIDDLE  ALT=\"slope+=+%28Y3-Y1%29%2F%28X3-X1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=slope+=+%28%28-2--1%29%2F%284-5%29%29+=+1 ALIGN=MIDDLE  ALT=\"slope+=+%28%28-2--1%29%2F%284-5%29%29+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >    ........................(2)<BR>\n" );
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document.write( "  From conditions (1) and (2)<BR>\n" );
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document.write( "  The 3 points do not a same line. <BR>\n" );
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document.write( "  For all points to lie on a line they should satisfy the equation of a line. Hence any two points taken on a line should calculate to the same slope of a line.<BR>\n" );
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document.write( "  Here the slopes are unequal hence the points do not lie on same line.<BR>\n" );
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document.write( "  To read more on equations of a line refer to articles on <A  rel=nofollow HREF=http://www.algebra.com/algebra/homework/Graphs/Graphing-by-Slope-Intercept-Method.lesson>wikipedia</A><BR>\n" );
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document.write( "since your points do NOT <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=lie ALIGN=MIDDLE  ALT=\"lie\"   DISABLED_style= \"max-width:90%; height:auto;\" > on a <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=single ALIGN=MIDDLE  ALT=\"single\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+straight ALIGN=MIDDLE  ALT=\"+straight\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+line ALIGN=MIDDLE  ALT=\"+line\"   DISABLED_style= \"max-width:90%; height:auto;\" >, they are NOT <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=collinear ALIGN=MIDDLE  ALT=\"collinear\"   DISABLED_style= \"max-width:90%; height:auto;\" >  </SPAN>\n" );
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