# change in graphic style - ConvexHull

I use this code to find the ConvexHull for some points:

pts2 = {{2, 1}, {5, 0}, {7, 0}, {9, 5}, {6, 8}, {0, 6}, {0, 4}};
Show[ConvexHullMesh[pts2, GridLines -> Automatic], Axes -> True]


the result is this pic:

I need the result like this:

Update

(included more style specifications as requested in the comments)

You can use BaseStyle to control the appearance of the convex hull, and you can extract the coordinates of a mesh by using mesh["Coordinates"]. Finally, Arrowheads can be used to style the axes:

pts2={{2,1},{5,0},{7,0},{9,5},{6,8},{0,6},{0,4}};

mesh = ConvexHullMesh[
pts2,
BaseStyle->{FrontFaceColor->None,EdgeColor->Black,FrontFaceOpacity->0}
];
Show[
mesh,
Graphics[{PointSize[Large],Point[mesh["Coordinates"]]}],
GridLines->Automatic,
Axes->True,
]


• Thanks, @Carl Woll How can I show the point in the vertex and change the lines color to be Black, also How to add the narrows on x-axes – Ateq Alsaadi Mar 27 '18 at 21:14

Another way is with MeshCellStyle.

pts2 = {{2, 1}, {5, 0}, {7, 0}, {9, 5}, {6, 8}, {0, 6}, {0, 4}};

ConvexHullMesh[pts2,
Axes -> True,
GridLines -> Automatic,
MeshCellStyle -> {0 -> {PointSize[Large], Opacity[1], Black},
1 -> {Thick, Black}, 2 -> None}
]


For whatever reason, the setting 2 -> None is influencing the vertices. This is why I manually set Opacity[1].

Here is an approximate facsimile:

ch = MeshPrimitives[ConvexHullMesh[pts2], 2];
bb = BoundingRegion[pts2];
cent = Mean[pts2];

Graphics[{{EdgeForm[Directive[Dashed, AbsoluteThickness[1]]], FaceForm[], bb},
{EdgeForm[Black], FaceForm[], ch},
{AbsolutePointSize[6], Point[pts2]},
{Text[Style["Γ", FontFamily -> "Times", FontSize -> 14], cent],
Text[TraditionalForm[Subscript["O", Row[{0, 0}]]], {0, 0}, {1.2, 1.2}],
Text[TraditionalForm[Subscript["O", Row[{∞, ∞}]]], Last[bb], -{1.2, 1.2}]},
{MapIndexed[Text[Subscript["γ", #2[[1]]], cent + 0.9 (Mean[#] - cent)] &,
Partition[ch[[1, 1]], 2, 1, 1]]}},
Axes -> True, AxesLabel -> {Style["μ", Medium], Style["ν", Medium]},
GridLines -> Automatic, GridLinesStyle -> Directive[Dotted, Opacity[1/4]],
Method -> {"AxesInFront" -> False, "GridLinesInFront" -> False},

    Graphics[Line /@ Partition[AppendTo[pts2, First[pts2]], 2, 1],

ListPlot[AppendTo[pts2, First[pts2]], PlotStyle -> {Black},