1997 Chevrolet Cavalier coolant leaking

Obviously I can't see it over a computer, but if you mean under the hood or under the car, on the passenger side, as opposed to on the front passenger side floor, the likely suspect is a leaking heater core. If you look on the passenger side of the firewall, under the hood, you'll see a 4"-long hose with a 90 degree bend hanging down. Coolant will drip from that if the heater core is leaking.

This is especially common on GM vehicles that still have the red Dex-Cool, (Dex-Mud) antifreeze in the system. That was falsely advertised as "lifetime" coolant so a lot of people never changed it. The additives wear out in about two years. That includes corrosion inhibitors that neutralize the acids that form in the coolant. Corroded radiators and heater cores are real common.