Is there a way to draw a set of lines in mathematica all with the same origin point?

Question

I have a set of points given by this list:

list1 = {{3, 1}, {1, 3}, {-1, 2}, {-1, -1}, {1, -2}};

I would like Mathematica to draw a line from the origin to all the points above. In other words draw vectors from the origin (0,0) to all the individual points in the above set. Is there a way to do this? So far I've tried the Filling option, PlotPoints and VectorPlot but they don't seem to be able to do what I want.

Answer 1

Starting easy, and then increasing difficulty:

Graphics[{Arrow[{{0, 0}, #}] & /@ list1}]

Graphics[{Arrow[{{0, 0}, #}] & /@ list1}, Axes -> True]

Needs["PlotLegends`"];
list1 = {{3, 1}, {1, 3}, {-1, 2}, {-1, -1}, {1, -2}};
k = ColorData[22, "ColorList"][[;; Length@list1]];

GraphicsRow[{
    Graphics[Riffle[k, Arrow[{{0, 0}, #}] & /@ #], Axes -> True], 
    Graphics@Legend[Table[{k[[i]], #[[i]]}, {i, Length@#}]]}] &@list1

Needs["PlotLegends`"];
list1 = {{3, 1}, {1, 3}, {-1, 2}, {-1, -1}, {1, -2}};
k = ColorData[22, "ColorList"][[;; Length@list1]];
ls = Sequence[Thick, Line[{{0, 0}, {1, 0}}]];

GraphicsRow[{
    Graphics[Riffle[k, Arrow[{{0, 0}, #}] & /@ #], Axes -> True], 
    Graphics@Legend[MapThread[{Graphics[{#1, ls}], #2} &, {k, #}]]}] &@list1

Needs["PlotLegends`"];
list1 = {{3, 1}, {1, 3}, {-1, 2}, {-1, -1}, {1, -2}};
pr = {Min@#, Max@#} & /@ Transpose@list1;
k = ColorData[22, "ColorList"][[;; Length@list1]];

GraphicsRow[{
    Graphics[r = Riffle[k, {Thick,Arrow[{{0, 0}, #}]} & /@ #], Axes -> True], 
    Graphics@
     Legend[MapThread[
             {Graphics[#1, Axes -> True, Ticks -> None, PlotRange -> pr], 
              Text@Style[#2, 20]} &, 
             {Partition[r, 2], #}]]}] &@list1

You could also tweak ListVectorPlot, although I don't see why you should do it, as it is not intended to use like this:

list1 = {{3, 1}, {1, 3}, {-1, 2}, {-1, -1}, {1, -2}};
data = Table[{i/2, -i/Norm[i]}, {i, list1}];
ListVectorPlot[data, VectorPoints -> All, 
                     VectorScale  -> {1, 1, Norm[{#1, #2}] &}, 
                     VectorStyle  -> {Arrowheads[{-.05, 0}]}]

Answer 2

Graphics[
 {
  Line[{{0, 0}, #}] & /@ list1
  }
 ]

where /@ is the shorthand infix notation for the function Map.

I wonder why you tried Filling, Plotpoints and VectorPlot. I must assume you haven't read the documentation at all, because even a superficial reading would tell you that those commands and options have nothing to do with the functionality you're looking for.