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You can put this solution on YOUR website!
Took a while, but I have a possible answer.
\n" ); document.write( "Let
\n" ); document.write( "(i) M = (0,0)
\n" ); document.write( "and
\n" ); document.write( "(ii) P = (1,5).
\n" ); document.write( "This makes the slope of MP = 5.
\n" ); document.write( "Now we need a coordinate for
\n" ); document.write( "(iii) N = (x,y)
\n" ); document.write( "such that
\n" ); document.write( "(iv) m(M,N) = 1/2
\n" ); document.write( "and
\n" ); document.write( "(v) m(N,P) = 2/3
\n" ); document.write( "----
\n" ); document.write( "from (i), (iii), and (iv)
\n" ); document.write( "(vi) m(M,N) = (y-0)/(x-0) = 1/2
\n" ); document.write( "(vii) x = 2y
\n" ); document.write( "----
\n" ); document.write( "from (ii), (iii), and (v)
\n" ); document.write( "(viii) m(N,P) = (y-5)/(x-1) = 2/3
\n" ); document.write( "and by substitution of (vii) into (viii) we get
\n" ); document.write( "(ix) y-5)/(2y-1) = 2/3
\n" ); document.write( "cross multiply to get
\n" ); document.write( "(x) 3y -15 = 4y - 2
\n" ); document.write( "subtract 3y and add 2 to get
\n" ); document.write( "(xi) y = -13
\n" ); document.write( "This means that x = -26 and our point N is
\n" ); document.write( "N = (-26, -13)
\n" ); document.write( "---
\n" ); document.write( "So in total we get
\n" ); document.write( "M = (0,0)
\n" ); document.write( "and
\n" ); document.write( "P = (1,5)
\n" ); document.write( "and
\n" ); document.write( "N = (-26,-13)
\n" ); document.write( "m(M,P) = 5/1 = 5
\n" ); document.write( "m(M,N) = 13/26 = 1/2
\n" ); document.write( "m(N,P) = 18/27 = 2/3 \n" ); document.write( "