Question

If the point D(-4, 6), E(1, 1) and F(x, y) are collinear, find the value if x + y.​

Answer 1

`\mathrm{Since\ the\ points\ D,E\ and\ F\ are\ collinear,\ the\ slope\ of\ line\ DE\ and\ EF}\\\mathrm{must\ be\ equal.}\\\mathrm{Let's\ find\ the\ slope\ of\ line\ DE.}\\\mathrm{m_(DE)}=(1-6)/(1-(-4))=(-5)/(5)=-1\\\mathrm{The\ slope\ of\ EF(m_(EF))}=(y-1)/(x-1)\\\mathrm{Now,}\\\mathrm{m_(DE)=m_(EF)}\\\mathrm{or,\ }-1=(y-1)/(x-1)\\\mathrm{or,\ }1-x=y-1\\\mathrm{or,\ }x+y=1+1\\\therefore x+y=2`