graphics - Barycentric coordinates

I am 100% new to mathematica and I don't really understand if I am doing this correctly. I have some most code except the calculation of the color. I will do that once I know I am doing this correctly. I am trying to make sure it is correct and if am not I need some direction as to what I am doing wrong. I added comments if that helps. Anything helps!

(* Triangle vertices *)

v1 = {-2.0, -2.0};
v2 = {2.0, -2.0};
v3 = {0.0, 2.0};

(* xy-space to plot *)


c1 = {1, 0, 0};
c2 = {0, 1, 0};
c3 = {0, 0, 1};   

I am trying to Compute the barycentric coordiantes of a 2D point xy based on triangle vertices v1, v2, v3 and that is what I need help on because I'm not sure that I got it right.

(* Input: xy = {x, y} and global v1, v2, v2 each as {x,y} *)
(* Output: uvw = {u, v, w}, the barycentric coordinates *)



(* The entries in the linear system set-up below need set. I Determine what  
   values in function *)

computeBaryCoords[xy_] := (
  mat = {{v1[[1]], v2[[1]], v3[[1]]}, {v1[[2]], v2[[2]], v3[[2]]}, {v1, v2, v3}};
  rhs = {xy[[1]], xy[[2]], mat};
  uvw = LinearSolve[mat, rhs];
  Return[uvw]
  );


computeColor[uvw_] := Return[ (* going to calculate colors *)]; 

range = 4;
plotTriangle = 
  Graphics[
    {EdgeForm[Thick], White, Polygon[{v1, v2, v3}], 
     PointSize[0.05], 
     RGBColor[c1], Point[v1], 
     RGBColor[c2], Point[v2], 
     RGBColor[c3], Point[v3]}, 

    Axes -> True, 
    PlotRange -> {{-range, range}, {-range, range}}];

Manipulate[(
  uvw = computeBaryCoords[xy];
  rgb = computeColor[uvw];
  plotPoint = 
    Graphics[
      {RGBColor[rgb[[1]], rgb[[2]], rgb[[3]]], PointSize[0.08],  Point[xy]}];
  plotBaryCoords =  

    Graphics[
      {Black 
       Text[Style["Barycentric Coordinates: ", FontSize -> 15], {0, 4}, Scaled[{1, 1}]], 
       Text[Style[NumberForm[uvw, 2], FontSize -> 15], {4, 4}, Scaled[{1, 1}]]}];
  Show[{plotTriangle, plotPoint, plotBaryCoords}]),
  {{xy, {0, 0}}, Locator}]