Draw blue and red lines alternatingly

Question

Given an array of points, I want to draw blue and red lines alternatingly.

Let $n\in\{0,1\}$, and arr be an array of points $$\textrm{arr} = \{ \{x_1, y_1\}, \{x_2,y_2\}, \ldots, \{x_n, y_n\}\}.$$ If $n=0$, I draw a blue line from the origin to $\{x_1, y_1\}$, then a red line from $\{x_1, y_1\}$ to $\{x_2, y_2\}$, then a blue line from $\{x_2, y_2\}$ to $\{x_3, y_3\}$, until the last line from $\{x_{n-1}, y_{n-1}\}$ to $\{x_{n}, y_{n}\}$.

If $n=1$, the blue and red lines are reversed. I draw a red line from the origin to $\{x_1, y_1\}$, then a blue line from $\{x_1, y_1\}$ to $\{x_2, y_2\}$, then a red line from $\{x_2, y_2\}$ to $\{x_3, y_3\}$, until the last line from $\{x_{n-1}, y_{n-1}\}$ to $\{x_{n}, y_{n}\}$.

For example, if

n=0
arr = {{1,0}, {2,0}, {3,0}}

then the result is

How can I make a function F[n,arr] returns a Lines object that draws the above?

Note: I tried a clumsy approach

colors[n_] := If[Mod[n, 2] == 1, Red, Blue]
F[n_, arr_] := Block[ {res = {}, newarr = Join[{{0, 0}}, arr]},
  For[i = 1; i <= Length[arr], i++, 
   Append[res, {colors[n + i], Line[newarr[[i]], newarr[[i + 1]]]}]];
  res]

With the above n and arr, I get an empty list (that is not what I want).

Answer 1

Clear["Global`*"];
SeedRandom[123];
arr = Prepend[RandomReal[1, {20, 2}], {0, 0}];
t := Sequence @@@ MapIndexed[
    {If[EvenQ[n + First@#2]
       , Red, Blue], Line[#1]} &
    , Partition[arr, 2, 1]];

GraphicsRow@Table[
  Graphics[t
   , Frame -> True
   , AspectRatio -> Automatic
   , Epilog -> {
     Text[
      Style[
       ToString@StringForm["n = ``", n]
       , 18]
      , {0.6, 0.9}]
     }
   ]
  , {n, {0, 1}}
  ]

Answer 2

listLinePlot[n_, data_, opts : OptionsPattern[]] := ListLinePlot[
     Partition[data, 2, 1], 
     PlotStyle -> RotateLeft[{Blue, Red}, n], 
     opts ]

Examples:

SeedRandom[123];
arr = Prepend[{0, 0}] @ RandomReal[1, {20, 2}];


listLinePlot[0, arr, PlotLabel -> Style["n = 0", 20]]

listLinePlot[1, arr, PlotLabel -> Style["n = 1", 20]]

Answer 3

theLines = Line /@ 
  Partition[Table[{RandomReal[], RandomReal[]}, {20}], 2, 1];
Graphics[
 Flatten@{{Red, #[[1]]}, {Blue, #[[2]]} } & /@ Partition[theLines, 2]]