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I'm brand new to Inkscape, and fairly brand new to SVG's in general. I'm trying to modify a map of the British Isles, https://upload.wikimedia.org/wikipedia/commons/6/62/British_Isles_location_map.svg

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Starting with something easy, the Isle of Man. Let's say I want to divide it in half.

I select a segment, add a bunch of nodes to it. Then using the "Edit paths by nodes (F2)" I can add a new blue edge through the island.

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Using "Break Apart", no dice. Using "Cut Path" or "Division", still nothing.

How can I cut the Isle of Mann into two pieces, without having a blue line running through it, like how Northern Ireland is

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I've also tried "Object to Path", nothing. "Stroke to Path" removes the white border, but doesn't actually divide the object into two separate objects.

What am I doing wrong? I've tried to follow instructions found on various Google Searches, but I can't figure this out.

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North Ireland and Isle of Man are costructed differently. Waterline of North Ireland is a separate object, the land itself is strokeless. I recolored the land shape to green.

enter image description here

Isle of Man is a single shape, its blue stroke is the waterline. Duplicate the isle. Remove the stroke from one. It's your land and it can be divided as you like. Let the other be on top without a fill as a stroke only object.

Here the fill only Isle of Man is divided and the northern half has got new color:

enter image description here

The division was made by drawing a line and then using Path > Division

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