document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1063614>Question 1063614</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Determine if the points (1,5),(2,3) and (-2,-11) are collinear. </SPAN>\n" );
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document.write( "Determine if the points (1,5),(2,3) and (-2,-11) are collinear.\r<BR>\n" );
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document.write( "Tutorial:<BR>\n" );
document.write( "The 3 points are collinear if they lie on the same line.<BR>\n" );
document.write( "First, we get get the equation of the line containing the first 2 points.<BR>\n" );
document.write( "We compute the slope of the points (1,5) and (2,3).<BR>\n" );
document.write( "The slope is equal to \"change in y\" divided by \"change in x\"<BR>\n" );
document.write( "slope, m = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283+-+5%29%2F%282+-+1%29+=+-2 ALIGN=MIDDLE  ALT=\"%283+-+5%29%2F%282+-+1%29+=+-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Next, we use the point-slope form <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+-+y%5B1%5D+=+m%28x+-+x%5B1%5D%29 ALIGN=MIDDLE  ALT=\"y+-+y%5B1%5D+=+m%28x+-+x%5B1%5D%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "We choose (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D ALIGN=MIDDLE  ALT=\"x%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5B1%5D ALIGN=MIDDLE  ALT=\"y%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >) = (1, 5)<BR>\n" );
document.write( "y - 5 = -2(x - 1)<BR>\n" );
document.write( "y - 5 = -2x + 2<BR>\n" );
document.write( "y = -2x + 7 is the equation of the line containing (1, 5) and (2, 3).<BR>\n" );
document.write( "Next, we check if the 3rd point (-2, -11) satisfies the equation y = -2x+7.<BR>\n" );
document.write( "If x = -2, then y = -2(-2)+7 = 11 (NOT equal to -11)<BR>\n" );
document.write( "Therefore, the 3 given points are NOT collinear<BR>\n" );
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