Try Counting

Since no two lines are parallel every line intersects every other line, which means the number of points created is $A=\binom{50}{2}=1225$ .

The total number of lines which can be created by $'A'$ points are $\displaystyle\binom{\binom{50}{2}}{2}$ .

But this doesn't give us the number of new lines created because some of the lines created by joining the new points lie on the existing lines. We need to subtract the unwanted ones. Observe that there will be 50 sets of 49 co-linear points. Thus number of new lines created are

$\displaystyle B=\binom{\binom{50}{2}}{2} - 50\times\binom{49}{2}=690900$

Thus $A+B=692125$ .

@Sravanth Chebrolu : How can we be sure that none of the points created are aligned - except in the obvious case were these points lie on one of the existing line ?

In the example below, it seems that i can construct 6 lines, no two of them being parallel, and no three of them meeting at the same point (to be checked). Yet, three of the points created are aligned (circled in red).

Do you agree ?