document.write( "Question 830754: If M (3,6) and N (9,0) what are the coordinates of the point L if it lies 2/3 of the way from M to N \n" ); document.write( "
Algebra.Com's Answer #500866 by josgarithmetic(39618)\"\" \"About 
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Part-way through the solution,\r
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\n" ); document.write( "\n" ); document.write( "The line MN :
\n" ); document.write( " m=(6-0)/(3-9)=-1.
\n" ); document.write( "if y=mx+b,then b=y-mx.
\n" ); document.write( "pick either point to get b.
\n" ); document.write( "b=0-(-1)9
\n" ); document.write( "b=9.
\n" ); document.write( "The line MN is \"y=-x%2B9\".\r
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\n" ); document.write( "\n" ); document.write( "Now, you want some point ON THE LINE MN, y=-x+9, which is 2/3 of the length distance from M(3,6). Use the distance formula, to first find the distance MN.\r
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\n" ); document.write( "\n" ); document.write( "\"MN+=+sqrt%28%280-6%29%5E2%2B%289-3%29%5E2%29\"
\n" ); document.write( "\"sqrt%2836%2B36%29\"
\n" ); document.write( "\"sqrt%2872%29\"
\n" ); document.write( "\"sqrt%282%2A36%29\"
\n" ); document.write( "\"MN=highlight_green%286%2Asqrt%282%29%29\"
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\n" ); document.write( "\"%282%2F3%29%2A%28MN%29=2%2Asqrt%282%29\"-------Use this as a target value, and use distance formula again; but now, you have some unknown point, (x,-x+9) and the known point, (3,6), and you want the distance between them to be \"2%2Asqrt%282%29\".\r
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\n" ); document.write( "\n" ); document.write( "If you understand all of that clearly, then you know what to do. Note, the variable point to be found, involves the line MN; the x coordinate as unknown, and the resulting y coordinate as -x+9.
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\n" ); document.write( "You will get two solutions for x and one of them will be what you want but the other will not be.
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