A plan of representation established as provided for in subsection (a) of § 10-46 and sections 10-63j to 10-63t, inclusive, shall be effective seven days after the referenda resulting in an affirmative majority vote in each of the participating towns. If the plan of representation requires a reduction in the number of members on a regional board of education from a participating town, a determination of the order in which the terms of members from such town shall be terminated shall be made on the basis of the length of the unexpired portion of their terms, with the terms of members having the shortest unexpired portions being terminated first until the number of members from the town complies with the plan. If two or more members of a town have the same unexpired portions of their terms, then within seven days after the date the plan is established, and under the supervision of the other members of the regional board, the member or members whose term or terms shall terminate shall be determined by lot. If the plan requires that additional members on the regional board of education be added from a town within the regional school district, the legislative body of the town shall fill the vacancies by appointment. A new member of the board so appointed by the legislative body of a town shall serve until a successor is elected and qualified at the next town election. The remaining members on a regional board of education whose terms are not affected by the plan of representation shall serve the unexpired portions of the terms for which they have been elected. Questions as to the terms of office of members on a regional board of education shall be determined by the regional board in accordance with the principles established in § 10-46.