Question 1150948

Let {{{C}}} be the point that divides {{{AB }}} in the ratio {{{1:3}}}.

{{{A}}}=({{{x[1]}}},{{{y[1]}}})=({{{-4}}},{{{4}}}),

{{{B}}}=({{{x[2]}}},{{{y[2]}}})=({{{6}}},{{{-5}}}) and 

{{{a:b=1:3}}}=>{{{a=1}}}, {{{b=3}}}


{{{C}}}=({{{(bx[1]+ax[2])/(a+b)}}},{{{(by[1]+ay[2])/(a+b)}}})

{{{C}}}=({{{(3*(-4)+1*6)/(1+3)}}},{{{(3*4+1*(-5))/(1+3)}}})

{{{C}}}=({{{(-12+6)/4}}},{{{(12-5)/4}}})

{{{C}}}=({{{-6/4}}},{{{7/4}}})

{{{C}}}=({{{-3/2}}},{{{7/4}}})

Here, 

{{{drawing ( 600, 600, -10, 10, -10, 10,
circle(-4,4,.12), circle(6,-5,.12),locate(-4,4,A),locate(6,-5,B),blue(line(-4,4,6,-5)),circle(-3/2,7/4,.12),locate(-3/2,7/4,C),
graph( 600, 600, -10, 10, -10, 10, 0)) }}}




Therefore, the point C({{{-3/2}}},{{{7/4}}})  divides {{{AB}}}  in the ratio {{{1:3}}}.