Convert to Mercator projection?

Attached I have a map... is there an easy way to make this projection Mercator? I am still a novice when it comes to mapping so any help would be greatly appreciated.

Oh and while we're at it, I must plot point on this map... but this code: "plotm(41,-103,'r','MarkerSize',20)" only makes an extremely small dot... despite adjusting MarkerSize..

Again, any assistance on both problems would be greatly appreciated!

figure
worldmap([30 50],[-110 -70]);
geoshow('Shapefiles/cb_2013_us_county_5m.shp', 'FaceColor', [.5 .5 1]);

Answer 1

[Chad Greene]

Converting projections after plotting doesn't usually work. To initialize a mercator map with those lat/lon limits, try this:

axesm('mercator','maplatlimit',[30 50],'maplonlimit',[-110 -70])
geoshow('usastatehi.shp')

[Chad Greene]

A workaround for the marker size issue, is you can specify a circle of given radius in kilometers or any other unit with circlem. Here's a red circle of 100 km radius.

axesm('mercator','maplatlimit',[30 50],'maplonlimit',[-110 -70])
geoshow('usastatehi.shp')
circlem(41,-103,100,'facecolor','red')

Answer 2

[Ryan]

Hello again Chad! Thank you for this. I ended up using "scatterm" which seemed sufficient for the image I wanted to generate. Thanks also for the tip on establishing map projection.