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I have two shapfile in QGIS to which I am trying to find the distances between. I have a shoreline which is a vector line and then I have hundreds of data points in the ocean. What I am trying to find is measuring the distance of each point to the corresponding place horizontally on the shoreline thus giving me a distance of each point from the shore. I have tried the distance matrix plugin which seems to only deal with point to point distances and have tried the mmqgis hub distance which only measures distances to a central fixed point on the line. Is there a plugin or way to find the distances I am looking for?

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The most convenient way to my mind is to import your layers into a spatial database such as Spatialite or PostGIS and use ST_Distance() SQL-querry.

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