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

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.