There is a great myth surrounding IP addresses. You can trace a network connection with an IP address, but you cannot trace a person or a computer.
IP addresses are like phone numbers on the internet. They are how one computer knows where to find another computer on a logical computer network. IP addresses were not designed to locate a computer geographically, but it is possible due to information volunarily provided by network operators.
Tracing an IP address sends a trace packet through a network, tracing it's hops until it reaches it's destination. Each hop may contain identifying information, such as the network operator and their address or location. This information is provided for reference, but it can be used to approximate the general location of the end target.
Here's what you can do with an IP trace:
Determine the general area of the target's location (City/region, state, country).
Determine what ISP they use.
Here's what you CANNOT do with an IP trace:
Determine the target's home address.
Identify the computer that is assigned that IP address.
Determine the identity of the person using the computer at that IP address.
Regardless of where you connect, your personal computer does not store information about who it is or where in the world it's located. Even if it did (which it doesn't), it won't send that information back when replying to ping requests. There is absolutely no way a person can pinpoint you or your computer's absolute location using just an IP address.
IP addresses are largely anonymous for home users. To extend the phone number analogy, think of an IP address as a phone number for a prepaid cell phone. You can use the number to contact the owner, but there is no owner information associated with the phone, nor is there an address or any other personally identifiable information. A computer/network can easily dump an IP address and acquire a new one in a matter of seconds.
You cannot "hide" your IP address. You can disguise it by using a proxy, or block trace pings with a firewall, but packets will ultimately reach your computer. There is no way to eliminate an IP address and have a working network at the same time. The internet cannot work without IP addresses, otherwise the remote computer will not know who to send the requested information back to.
Dumb little script kiddies make up all these scary rumors about IP addresses, and threaten to hack your IP address, come to your house, and drink all your Mountain Dew, but it's just not true. An IP address is an address, a means to locate something... but it is an Internet Protocol address that works only on the Internet; it is not a mailing address or geographical address. People see "addresss" and think someone can find them, and a cyber-bully will use that uncertainty against people.