Notwithstanding the provisions of § 10.1-507, the Board may, in its discretion, relocate or redefine district boundaries on its own motion pending or subsequent to any annexation or consolidation. If the Board determines on its own motion to relocate or redefine district boundaries, the Board shall serve written notice of its determination, containing the full terms of the proposed relocation or redefinition, on the governing body of each district, county, city and town affected by the relocation or redefinition of boundaries. If within forty-five days from the date of service of such notice each governing body affected approves the Board’s action by resolution of a majority of the members, the Board may then proceed to act on its motion without a public hearing.