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Is there a tool or plugin in QGIS to extend line features up to their intersection point? enter image description here

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Perhaps you can do it with some of the CAD plugins of QGIS. For sure you can do it with Kosmo GIS http://opengis.es/

Select to linestrings which should be extended and use the Expand lines until crossing tool from the CAD toolbox. CAD Tools extension must be activated first from the Extension manager.

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Click on the map.

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For the second case use another CAD tool "Extend line"

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Extend to nearby feature option suits for this use case

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Click close to the line that should be connected

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CADDigitize now comes with a trim/extend function.

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