Lita på means "to trust " or "to rely/be confident in someone." If you wanted to say "depend on" on more clearly, you would use the verb bero.
It's a similar construction as the Swedish sentence. The only difference is the preposition 'på' being necessary in Swedish, whilst in English the preposition 'in' is optional. That is, in English you can use both "I trusted you" and "I trusted in you". In Swedish you have to use "Jag litade på dig".
To answer your question more accurately though, trusting in someone and trusting someone are essentially the same thing. In English, I guess the idea is that you put your faith/trust into the person (hence 'in'), while in Swedish the idea is that you lay your faith/trust onto or upon the person (hence 'på'). This is all to say that they're both phrasal verbs with prepositions in Swedish and English, but you don't need the preposition in English although it has more emotional impact if you include it.
Hope that helps!
did is used for purely grammatical reasons in questions and negated sentences. But in an ordinary sentence like this one, it adds a nuance of meaning that is not in the Swedish sentence.
There's a problem with getting the machinery to accept any kind of spelling variation in the dictation exercises. We can't do anything about this.
If the casual spelling dej isn't accepted when translating, report it via the Report a problem button.