Final answer:
The network administrator uses the 'show ip interface brief' command to check the status of the switch interfaces and the IP address on interface VLAN 1, but it is not used to verify host reachability, path to a host, or the switch's default gateway.
Step-by-step explanation:
When a network administrator issues the show ip interface brief command on a switch, they are primarily checking the status of the switch interfaces and the address configured on interface vlan 1. This command is useful for quickly verifying which interfaces are up or down, and if they are administratively down. It is also a convenient way to see which IP addresses are assigned to switch interfaces, particularly the management interface (VLAN 1), on a small campus network.
The command does not directly check reachability to a specific host on another network (option b), the path used to reach a specific host on another network (option c), or the default gateway used by the switch (option d). Although information about interface status can indirectly help in troubleshooting network reachability and path issues, the show ip interface brief command is not used expressly for these purposes.