A family member thinks I am lying about where I am going but I'm not, what should I do?

It's something that occurs in all families. Whomever is just being protective, trying to shake you to hear if with time your going out story changes. If you're being truthful, then you have no worries

Perhaps take a selfie of where you are as proof. Even on snapchat you have the option of putting on a time filter to show exactly where and when you are some place. If not, you could provide your parents with a friends contact which they can call just to make sure. Or get them to call you and they can speak to a friend who can verify your whereabouts. The best thing to do is not to get angry and just say calmly where you are going.

I guess there is no other way then tell them over and over again that you are not lying. Maybe you can take some photos and send or show them to them so they believe you.

Try to ask them why they feel that way, may be there is a reason and u may be able to clear the misunderstanding

You need to show your family member that you are responsible and trustworthy! If they allow you to go they'll see that you aren't betraying their trust or being deceitful.

talk sincerely with that person and show him that can trust you whenever you go, or take a picture and send him

If you haven't done anything to deserve the distrust, ignore. Else, ensure they know (GPS/check in/staying available and informing once you reach)

You could show them, take them with you as proof. Maybe spend time with them too, the problem might not be that they don't believe you but they are jealous and what to spend time with you too.

Maybe the best approach is to start a dialog wit the member what are the reasons for not believing you. After that you will be clear what kind of behavior

Once you go out take him or her with you and let him or her trust you If he or she trusts you it will be solved