I've created a point data layer in QGIS using a .png image as a template. Of course the .png had no projection, and when creating the new shapefile I chose the WGS_84 coordinate system. Now, I need these data points to 'match up' with a (correctly projected) shapefile of Ireland in ArcMap 10.2. When adding the newly created data, I got a message stating something along the lines of the shapefile not being the same extent as the other data and that projecting the data may result in unexpected behavior. So the data points have been projected in some ocean judging by the basemap, and using the Data and Projections > Batch Project tool to change the PCS to TM65 (the Irish National Grid) has not rectified this.
Is it possible to change the coordinates of each point (there are over 100 at this stage...) to align with a shapefile of Ireland, or do I just have to start from scratch and create the points again, this time over the shapefile? Also, would I be able to align .png files with the Ireland shapefile to prevent this predicament for the next batch of data points I am going to create?