I'm going to try to get revenge on a cheater.
How are you hoping to get revenge on a cheater?
I'll find a way to hurt them.
It's understandable that you feel hurt about being cheated on but seeking revenge isn't good.
They should pay for hurting me though.
It's tempting to want to get revenge on people that hurt us but be aware that as long as you are thinking of vengeance you're not able to get on with your own life. If you did finally get revenge on them you would find that it wouldn't give you happiness, it's better just to move on.