How can you remain positive when you're surrounded by negative people?

It is indeed a very difficult position to be in. I do not know how you or your family is, or what kind of behaviours or attitudes they display. One thing you do say is that they put a downer on everything. So let me assume here that they find it hard to believe when something is good, or someone shows kindness, thinking that there is an agenda behind it. So how to remain positive, that is, to believe in goodness and kind-heartedness, when your family doesn't?

Well, let's start with where you are, right now. Let's look at the positive. You are here, you are alive, and you can see yourself being 'engulfed' by this negativity. The positive is that you haven't - it is a struggle for sure-  but you are aware of the situation and how hard it is to remain positive.  So from here there are several things you can do. One is to continue to be aware of their negativity, and how that affects you, and your relationship with them. Make it into a story: journal -write every day about it- talk to friends about it, or even a therapist. Another is to keep and create connections outside the family, they will provide a much needed contrast to your family and hopefully a safe space where you will be able to talk  about what is going on in the house; it will also provide inspiration and energy to keep going, and ultimately, a way out.

One way to look at these situations, is that family units are bound to disperse, such is the nature of things: offsprings sooner or later leave the house... and sometimes this is because the situation inside the family become unbearable. This pressure starts to build where it forces you to look outside and nurture yourself of ideas and connections that align with what you believe to be true, that excite you, that make you want to live and thrive. So in some way, the 'negative' family is forcing you to become yourself, to differentiate, to want to get out and be yourself. While this can be very uncomfortable or even worse, the end result is the flowering of something unique, which is whatever you turn out to be. 

As you grow to be yourself and start to get the confidence to show your family who you are (boundaries!) I could expect there to be a certain amount of backlash from them. They can further put pressure on you to conform to their ways, and this can have the opposite effect of distancing you further from them. Families usually require some kind of loyalty, and sometimes this can be quite unconscious. This means that sometimes to distance oneself from the family can become very hard because we have internalized this loyalty - and it can be very difficult to against it -but not impossible.

I hope you can remain positive, to keep on looking for answers outside, to keep reaching out as you have done just now. Answers will come. Keep trusting yourself -even if that goes against your family's values-  To be oneself and not let yourself be dragged down by your own family is possibly one of the most epic struggles an individual can have. So it's important to recognize this and to give yourself a big hug and reassurance that you are on the right track. All the best to you.