The Housing Corporation of Arlington is celebrating the completion of renovations to the first of three buildings that the nonprofit organization is converting into affordable housing in its Capitol Square Apartments project. The building, part of the complex at Massachusetts Avenue and Elmhurst Road in East Arlington, provides housing for families making no more than 60 percent of the area’s median income, which is $44,100 for a family of two. An application process for prospective tenants was held last month. The $11 million project is being paid for using private and public funds, and will create a total of 32 housing units in the three buildings, which are about 100 years old. There will be a mix of studio, one-bedroom and two-bedroom apartments. A ribbon-cutting ceremony for the first building on Dec. 12 was attended by about 100 supporters, according to the organization.