Question 741263
if the points A({{{1}}},{{{-1}}}), B({{{4}}},{{{-2}}}) and C({{{16}}},{{{1}}}) are collinear, they will lie  in a straight line;


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}}} slope}}}

Hence it will be sufficient to prove that the slope calculated taking {{{2 }}} points at a time should be equal.


Slope of line taking points (x1,y1)= ({{{1}}},{{{-1}}}) and (x2,y2)=({{{4}}},{{{-2}}}) is

{{{slope=(y2-y1)/(x2-x1)}}}

{{{slope=(-2-(-1))/(4-1)}}}

{{{slope=(-2+1)/3}}}

{{{slope=-1/3}}}

{{{slope=-0.333}}}


Slope of line taking points (x1,y1)= ({{{1}}},{{{-1}}}) and (x2,y2)=({{{16}}},{{{1}}}) is

{{{slope=(y2-y1)/(x2-x1)}}}

{{{slope=(1-(-1))/(16-1)}}}

{{{slope=(1+1)/15}}}

{{{slope=2/15}}}

{{{slope=0.133}}}

since {{{-0.333<>0.133}}}, given points are NOT collinear


{{{drawing(500,500,-10,20,-5,5,grid(0),circle(1,-1,0.2),circle(16,1,0.2),circle(4,-2,0.2),graph(500,500,-10,20,-5,5))}}}