You're given two lines with their two coordinates each, how to find the coordinate at they will eventually meet?

Question

Assuming the lines are not parallel and coinciding. So a similar to this;

So with those four coordinates only, how to find (a,b)

Answer 1

The equation of the first line is $$ y - y_1 = \frac{y_2 - y_1}{x_2-x_1}\left(x - x_1 \right) $$ and similarly of the second line is $$ y - y_3 = \frac{y_4 - y_3}{x_4-x_3}\left(x - x_3 \right) $$ equating $y$-values at the intersection point gives us the linear equation in $x$ $$y_1 + \frac{y_2 - y_1}{x_2-x_1}\left(x - x_1 \right) = y_3 + \frac{y_4 - y_3}{x_4-x_3}\left(x - x_3 \right) $$ Can you take it from here?