D is the intersection of AD and CD.
The diagram shows a quadrilateral ABCD.
The equations of side AD and CD are 13x-9y+54=0 and x-3y-12=0 respectively. Use the equation 13x-98y+54+k(x-3y-12) to find the equation of the diagonal BD in general form.
How exactly do I find point D to do this question?
I just read the question again more carefully and after much thought i concluded that I have no idea what it is getting at. The quadrilateral is irrelevant: the points A and C convey no extra information about the diagonal and the equation... isn't even an equation, let alone being useful in any way I can see.
Sorry but I have no idea what method you are expected to use.
You can find D by using simultaneous equations with AD and BC and then find BD using the normal methods (rise over run or simultaneous equations; whichever).
By the way, the point A should be on the y-axis in your diagram, but this is probably irrelevant.