If the highway commissioner, or upon appeal from his decision, the county superintendent of highways, shall enter a preliminary order for the laying out, widening, alteration or vacation of a township or district road, the highway commissioner or county superintendent of highways, as the case may be, shall cause a survey and plat of such township or district road to be made by a competent surveyor who shall report such survey and plat to the highway commissioner or county superintendent, as the case may be, giving the courses and distances and specifying the land over which such road is to pass; in which he may make such changes between the termini of the road described in the petition, as the convenience and interest of the public in his judgment may require. Upon the petition of 12 land owners residing in the district where the road is situated, it shall be the duty of the highway commissioner or county superintendent, as the case may be, within a reasonable time to employ a competent surveyor and have any road designated in such petition to be once resurveyed.