Final answer:
The new family of plants with swimming sperm and vascular tissue would be classified in Phylum Pterophyta, as these traits are indicative of ferns and their relatives.
Step-by-step explanation:
The plants with swimming sperm and vascular tissue would be classified in the Phylum Pterophyta.
Swimming sperm is a characteristic feature of both bryophytes (such as mosses and liverworts) and pterophytes (such as ferns), which require water for reproduction because the male gamete uses flagella to swim to the female gamete. Unlike bryophytes, pterophytes have developed vascular systems, which allow for the transport of water and nutrients, thus supporting larger plant structures. Neither angiosperms nor gymnosperms have swimming sperm; they rely on pollination mechanisms that do not require water.
While angiosperms produce flowers and fruits, and gymnosperms like conifers produce seeds in cones, neither of these traits is mentioned in the question. Therefore, the mentioned family of plants, possessing both swimming sperm and vascular tissue, fits best in Phylum Pterophyta, indicative of an evolutionary step between non-vascular plants and seed-bearing vascular plants like gymnosperms and angiosperms.