The latest design plans for extending the Somerville Community Path south into East Cambridge will be shown at a meeting next week. The path’s growth is part of the Green Line Extension Project, which will stretch the MBTA trolley line from Cambridge's Lechmere station through Somerville to a new terminal stop near Tufts University in Medford. Heading south, the community bicycle and pedestrian path currently ends at Lowell Street in Somerville. The extension to East Cambridge would cover more than 2 miles. Members of the Green Line Extension Project planning team will give a public presentation on the path from 6 to 8 p.m. Tuesday at the Holiday Inn Boston-Somerville, 30 Washington St.