solution scribbles

> A :=[0,0]; B:=[b1,b2]; C:=[1,0];

> X := t*B;

> Y := s*B+(1-s)*C;

> eqn := evalm(w*X + (1-w)*Y ) ;

> sol :=solve(eqn[2],{w});

> Z :=simplify(subs(sol,evalm(eqn)));

> drawit := (b1,b2,t,s) ->display([
plot([[0,0],[b1,b2],[1,0],[0,0]],color=red,thickness=3),
plot([t*[b1,b2], s*[b1,b2]+(1-s)*[1,0],[-t*(-1+s)/(t-s), 0] ],color=black,thickness=3)],scaling=constrained) ;

> drawit(-1,1.3,.7,.4);