Something like that?
detectEndPoints := { {RandomReal[{0, 4}], RandomReal[{0, 5}]}, {RandomReal[{0, 4}], RandomReal[{0, 5}]}}; segments = Table[detectEndPoints , {1000}]; (* Graphics[Line /@ segments] Old Way *) Graphics[Line @ segments] (* Valid since V6. Thanks @Mark McClure *)

NTN!
Edit
Repeating your question, I'm not sure if you are generating a continuous line by defining one endpoint at a time or a set of unconnected segments (as indicated above). Just in case, you go the continuous way:
detectEndPointsV2[i_] := {Cos[2 Pi i 17/100], Sin[2 Pi 17 i/100]}; segments = Table[detectEndPointsV2[i], {i, 101}]; Graphics[ Line@segments ]

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