Is there a way to add Triton 1X from a Triton 100X, to my DNA extraction mix without having to dilute the Triton 100X? My professor says it is possible, but I have no clue about that.
I think there's a bit of a misunderstanding. Triton X-100 is the name of the chemical, while Triton 100X implies a dilution factor (One hundred times the amount of Triton that you need for a given solution).
If your DNA extraction mix is 1000ul, then you will add 10ul of (100X) Triton X-100 to give you (1X) Triton X-100 in final DNA extraction mix.
Similarly, if your DNA extraction mix is 500ul, then you will add 5ul of (100X) Triton X-100 to give you (1X) Triton X-100 in final DNA extraction mix.