No plat of or instruments effecting the subdivision of real property described in section 19-918 shall be recorded or have any force and effect unless such plat is approved by the city council or village board of trustees of such municipality or its agent designated pursuant to section 19-916. The city council or village board of trustees of such municipality shall have power, by ordinance, to provide the manner, plan, or method by which real property in any such area may be subdivided, platted, or laid out, including a plan or system for the avenues, streets, or alleys to be laid out within or across the same, and to prohibit the sale or offering for sale of, and the construction of buildings and other improvements on, any lots or parts of real property not subdivided, platted, or laid out as required in sections 19-918 and 19-920.