Question

Given a set of points in the plane T={a1,a2,...,an} then Graphics[Polygon[T]] will plot the polygon generated by the points. How can I add labels to the polygon’s vertices? Have merely the index as a label would be better then nothing. Any ideas?

Answer 1

pts = {{1, 0}, {0, Sqrt[3]}, {-1, 0}};
Graphics[
 {{LightGray, Polygon[pts]},
  {pts /. {x_, y_} :> Text[Style[{x, y}, Red], {x, y}]}}
 ]

To add point also

pts = {{1, 0}, {0, Sqrt[3]}, {-1, 0}};
Graphics[
 {{LightGray, Polygon[pts]},
  {pts /. {x_, y_} :> Text[Style[{x, y}, Red], {x, y}, {0, -1}]},
  {pts /. {x_, y_} :> {Blue, PointSize[0.02], Point[{x, y}]}}
  }
 ]

update:

Use the index:

pts = {{1, 0}, {0, Sqrt[3]}, {-1, 0}};
Graphics[
 {{LightGray, Polygon[pts]},
  {pts /. {x_, y_} :> 
     Text[Style[Position[pts, {x, y}], Red], {x, y}, {0, -1}]}
  }
 ]