Split a CONVEX polygon into 2 parts vertically (python)

I have an array of points which represent the vertices of a CONVEX polygon. example: [[1,0],[3,0],[4,2],[0,5],[2,8]]

Now I am trying to do is split the polygon into 2 equal parts from its longest side (vertically). For example as the image shows below: Also it doesn't have to be exactly equal areas it can be a close number to 2 halves. The image shows what kind of cut I am looking for. The red line could have cut horizontally using y axis but polygon was more stretched and long on the x axis so it split it on x axis.

Also I am JUST looking for 2 split no more than that.

[IMAGE]

i tried to search online for some solutions but wasn't able to find a proper resource.